Answer:
2 m/s
Explanation:
The electromagnetic flow-metre work on the principle of electromagnetic induction. The induced voltage is given as
[tex]E = Blv[/tex]
where [tex]E[/tex] is the induced voltage = 2.88 mV = 2.88 x 10^-3 V
[tex]l[/tex] is the distance between the electrodes in this field which is equivalent to the diameter of the tube = 1.2 cm = 1.2 x 10^-2 m
[tex]v[/tex] is the velocity of the fluid through the field = ?
[tex]B[/tex] is the magnetic field = 0.120 T
substituting, we have
2.88 x 10^-3 = 0.120 x 1.2 x 10^-2 x [tex]v[/tex]
2.88 x 10^-3 = 1.44 x 10^-3 x [tex]v[/tex]
[tex]v[/tex] = 2.88/1.44 = 2 m/s
A car starts from rest and accelerates with a constant acceleration of 5 m/s2 for 4 s. The car continues for 18 s at constant velocity. How far has the car traveled from its starting point
A5 kg box slides 3 m across the floor before coming to rest. What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3 m / s?
Answer:
Coefficient of kinetic friction (Cof. KE) = 0.153
Explanation:
Given:
Mass of box (M) = 5 kg
Distance = 3 m
Initial speed (v) = 3 m/s
Find:
Coefficient of kinetic friction (Cof. KE)
Computation:
v² = u² + 2as
a = v² / 2s
a = 9 / 2(3)
a = 1.5 m/s²
Coefficient of kinetic friction (Cof. KE) = a / g
Coefficient of kinetic friction (Cof. KE) = 1.5 / 9.8
Coefficient of kinetic friction (Cof. KE) = 0.153
In Young's 2-slit interference experiment, the wavelength of laser light can be determined. The two slits are separated by 0.16 mm. The screen is 1.4 m from the slits. It is observed that the second bright band is located 11 mm from the center of the pattern. Given this information, what is the wavelength of the laser light?
a. 1258 nm
b. 419 nm
c. 500 nm
d. 629 nm
Answer:
d. 629 nm
Explanation:
slit separation d = .16 x 10⁻³ m
distance of screen D = 1.4 m
distance of second bright band = 11 x 10⁻³
distance of second bright band = 2 x band width
= 2 x λ D /d
Putting the values given ,
11 x 10⁻³ = 2 x λ x 1.4 / .16 x 10⁻³
λ = 1.76 x 10⁻⁶ / 2.8
= .6285 x 10⁻⁶
= 628.5 x 10⁻⁹
= 629 nm approx .
The frequency of light emitted from hydrogen present in the Andromeda galaxy has been found to be 0.10% higher than that from hydrogen measured on Earth.
Is this galaxy approaching or receding from the Earth, and at what speed?
Answer:
3x10^5m/s
Explanation:
See attached file
Explanation:
The speed of the light emitted from the earth is approaching the galaxy at [tex]3\times 10^5\;\rm m/s[/tex].
Doppler's Effect
According to the Doppler effect, the difference between the frequency at which light wave leave a source and reaches an observer is caused by the relative motion of the observer and the wave source.
Given that the difference in the frequency is 0.10 %. The speed of light emitted from the galaxy can be calculated by the Doppler effect.
[tex]\dfrac {\Delta f}{f} = \dfrac {v}{c}[/tex]
Where f is the frequency of the light, v is the speed of light emitted from the galaxy and c is the speed of light emitted from the earth.
[tex]\dfrac {0.10 f}{100 f} = \dfrac {v}{3\times 10^8}[/tex]
[tex]v = 3\times 10^5\;\rm m/s[/tex]
Hence we can conclude that the speed of the light emitted from the earth is approaching the galaxy at [tex]3\times 10^5\;\rm m/s[/tex].
To know more about the doppler effect, follow the link given below.
https://brainly.com/question/1330077.
Rod cells in the retina of the eye detect light using a photopigment called rhodopsin. 1.8 eV is the lowest photon energy that can trigger a response in rhodopsin. Part A What is the maximum wavelength of electromagnetic radiation that can cause a transition
Answer:
The maximum wavelength of the e-m wave is 6.9 x 10^-7 m
Explanation:
Energy required to trigger a response = 1.8 eV
we convert to energy in Joules.
1 eV = 1.602 x 10^-19 J
1.8 eV = [tex]x[/tex] J
[tex]x[/tex] = 1.8 x 1.602 x 10^-19 = 2.88 x 10^-19 J
The energy of an electromagnetic wave is gotten as
E = hf
where
h is the Planck's constant = 6.63 x 10^-34 J-s
and f is the frequency of the wave.
substituting values, we have
2.88 x 10^-19 = 6.63 x 10^-34 x f
f = (2.88 x 10^-19)/(6.63 x 10^-34)
f = 4.34 x 10^14 Hz
We know that the frequency of an e-m wave is given as
f = c/λ
where
c is the speed of light = 3 x 10^8 m/s
λ is the wavelength of the e-m wave
From this we can say that
λ = c/f
λ = (3 x 10^8)/(4.34 x 10^14)
λ = 6.9 x 10^-7 m
I WILL GIVE BRAINLIEST Identify two types of motion where an object's speed remains the same while it continues to change direction
Answer:
velocity and acceleration
Answer:
Hey there!
Centripetal (Circular Motion) and Oscillating Motion.
Let me know if this helps :)
Complete each of the statements
A. Lines of force are lines used to represent ________ an ________ electric field
B. The intensity of an electric field is the coefficient between the _________ that in the field exerts on a test ___________ located at that point and the value of said charge
C. The electric field is uniform if at any point in the field its _________ and ________ is the same
D. The van der graff generator is a _________ machine which has two __________ that are driven by a _________ that generates a rotation
Answer:
A: magnitude and direction
B: Force that the field exerts on a test charge
C: its magnitude and direction is the same.
D: electrostatic machine
two rollers that are driven by a motor that generates a rotation
Explanation:
What happens to the magnetic field when you reverse the direction of current by sliding the battery voltage bar past 0 volts
Answer:
The polarity of the magnetic field changes
Explanation:
This because The magnetic field generated is always perpendicular to the direction of the current and parallel to the solonoid. Hence if we reverse the current the direction of magnetism also reverses. In other words the magnetic poles gets reversed (North pole becomes south pole and the south pole becomes the north pole)
To protect her new two-wheeler, Iroda Bike
buys a length of chain. She finds that its
linear density is 0.68 lb/ft.
If she wants to keep its weight below 1.4 lb,
what length of chain is she allowed?
Answer in units of ft.
Answer:
1.8/0.61 =2.95 ft
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
;)
Given a double slit apparatus with slit distance 2 mm, what is the theoretical maximum number of bright spots that I would see when I shine light with a wavelength 500 nm on the slits
Answer:
The values is [tex]m_{max} = 8001 \ bright \ spots[/tex]
Explanation:
From the question we are told that
The slit distance is [tex]d = 2 \ mm = 2*10^{-3} \ m[/tex]
The wavelength is [tex]\lambda = 500 \ nm = 500 *10^{-9} \ m[/tex]
At the first half of the screen from the central maxima
The number of bright spot according to the condition for constructive interference is
[tex]n = \frac{d * sin (\theta )}{\lambda}[/tex]
For maximum number of spot [tex]\theta = 90^o[/tex]
So
[tex]n = \frac{2*10^{-3} * sin (90 )}{500 *10^{-9}}[/tex]
[tex]n =4000[/tex]
Now for the both sides plus the central maxima we have
[tex]m_{max} = 2 * n + 1[/tex]
substituting values
[tex]m_{max} = 2 * 4000 + 1[/tex]
[tex]m_{max} = 8001 \ bright \ spots[/tex]
A microwave oven operates at a frequency of 2400 MHz. The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly
downward toward the base. The base is lined with a material that completely absorbs microwave energy. The total microwave energy content of the cavity is 0.50 mJ.
A)The power output of the microwave oven is?
B) The intensity of the microwave beam is?
C) The electric field amplitude is?
D) The force on the base due to the radiation is?
Answer:
power = 600000 W
intensity = 6666666.66 W/m²
Em = 70880.18 N/m
F = 2 × [tex]10^{-3}[/tex] N
Explanation:
given data
frequency f = 2400 MHz
height oven cavity h = 25 cm = 0.25 m
base area measures A = 30 cm by 30 cm
total microwave energy content of cavity E = 0.50 mJ = 0.50 × [tex]10^{-3}[/tex]
solution
first, we get here total time taken from top to bottom that is express as
Δt = [tex]\frac{h}{c}[/tex] ...............1
Δt = [tex]\frac{0.25}{3\times 10^8}[/tex]
Δt = 8.33 × [tex]10^{-10}[/tex] s
and
power output will be
power = [tex]\frac{E}{\Delta t}[/tex] ..............2
power = [tex]\frac{0.50 \times 10^{-3}}{8.33 \times 10^{-10}}[/tex]
power = 600000 W
and
intensity of the microwave beam is
intensity = power output ÷ base area ..............2
intensity = [tex]\frac{600000}{30 \times 30 \times 10^{-4}}[/tex]
intensity = 6666666.66 W/m²
and
electric field amplitude is
as we know intensity I = [tex]\frac{E^2}{c \mu o}[/tex] ...............3
[tex]E(rms) = \sqrt{Ic\ \mu o} \\E(rms) = \sqrt{6666666.66 \times 3 \times 10^{8} \times 4 \pi \times 10^{-7} }[/tex]
E(rms) = 50119.87 N/m
and we know
[tex]E(rms) = \frac{Em}{\sqrt{2}}\\50119.87 = \frac{Em}{\sqrt{2}}[/tex]
Em = 70880.18 N/m
and
force on the base due to the radiation is by the radiation pressure
[tex]Pr = \frac{l}{c}[/tex] ..................4
[tex]\frac{F}{A} = \frac{l}{c}[/tex]
so
F = [tex]\frac{6666666.66 \times 900 \times 10^{-4}}{3\times 10^8}[/tex]
F = 2 × [tex]10^{-3}[/tex] N
An airplane flies 1,592 miles east from Phoenix, Arizona, to Atlanta, Georgia, in 3.68 hours.
What is the average velocity of the airplane? Round your answer to the nearest whole number.
Answer:
433
Explanation:
14 A particle of mass m strikes a vertical rigid wall perpendicularly from the left with velocity v.
rigid wall
If the collision is perfectly elastic, the total change in momentum of the particle that occurs as a
result of the collision is
A. 2mv to the right.
B. 2my to the left.
C. my to the right.
D. my to the left.
Answer:
C. mv to the right
Explanation:
momentum of thr particle=m1v1
momentum of the wall=m2v2
m1v1+ m2v2 =m1u1+ m2u2 since the wall doesn't move it's momentum is zero.
m1v1 =m1u1
therefore change in that occurs as result of the collision is C. mv to the right
The total change in momentum of the particle of mass m that collides elastically with a vertical rigid wall perpendicularly from the left with velocity v is 2mv to the left (option B).
The total change in momentum is given by:
[tex] \Delta p = p_{f} - p_{i} [/tex]
In the initial state, the particle is moving to the right until it collides with the rigid wall, so:
[tex] p_{i} = mv [/tex]
In the final state, the particle moves backward after the collision with the wall, so:
[tex] p_{f} = -mv [/tex]
The minus sign is because it is moving in the negative x-direction (to the left)
Hence, the total change in momentum is:
[tex] \Delta p = -mv - mv = -2mv [/tex]
Therefore, the total change in momentum of the particle is 2mv to the left (option B).
Find more here:
https://brainly.com/question/6391301?referrer=searchResultshttps://brainly.com/question/24592032?referrer=searchResults
I hope it helps you!
how many electrons do calcium have in their outer shell
Answer:
Calcium has two electrons in its outer shell.
Explanation:
Calcium is defined as a metal due to its physical and chemical traits. The two outer electrons are very reactive. Calcium has a valence of 2.
Calculate the time it would take a cell phone signal to travel from a point on the equator to the satellite and back.
A 0.100-kg metal rod carrying a current of 15.0 A glides on two horizontal rails 0.550 m apart and 2.0 m long,
(a) If the coefficient of kinetic friction between the rod and rails is 0.120, what vertical magnetic field is required to keep the rod moving at a constant speed?
(b) If the friction between the rod and rail is reduced zero, the rod will accelerate. If the rod starts from rest at the one end of the rails, what is the speed of the rod at the other end of the rails for this frictionless situation? Use the same field value you calculated in part (a).
Answer:
The speed of the rod is 2.169 m/s.
Explanation:
Given that,
Mass = 0.100 kg
Current = 15.0 A
Distance = 2 m
Length = 0.550 m
Kinetic friction = 0.120
(a). We need to calculate the magnetic field
Using relation of frictional force and magnetic force
[tex]F_{f}=F_{B}[/tex]
[tex]\mu mg=Bli[/tex]
[tex]B=\dfrac{\mu mg}{li}[/tex]
Where, l = length
i = current
m = mass
Put the value into the formula
[tex]B=\dfrac{0.120\times0.1\times9.8}{0.550\times15.0}[/tex]
[tex]B=0.01425\ T[/tex]
[tex]B=1.425\times10^{-2}\ T[/tex]
(b). If the friction between the rod and rail is reduced zero.
So, [tex]f_{f}=0[/tex]
We need to calculate the acceleration
Using formula of force
[tex]F_{net}=f_{f}+F_{B}[/tex]
[tex]F_{net}=0+Bil[/tex]
[tex]ma=Bil[/tex]
[tex]a=\dfrac{Bil}{m}[/tex]
Put the value into the formula
[tex]a=\dfrac{1.425\times10^{-2}\times15\times0.55}{0.1}[/tex]
[tex]a=1.176\ m/s^2[/tex]
We need to calculate the speed of the rod
Using equation of motion
[tex]v^2=u^2+2as[/tex]
Put the value into the formula
[tex]v^2=0+2\times1.176\times2[/tex]
[tex]v^2=\sqrt{4.704}\ m/s[/tex]
[tex]v=2.169\ m/s[/tex]
Hence, The speed of the rod is 2.169 m/s.
A 70 kg human body typically contains 140 g of potassium. Potassium has a chemical atomic mass of 39.1 u and has three naturally occurring isotopes. One of those isotopes, 40K,is radioactive with a half-life of 1.3 billion years and a natural abundance of 0.012%. Each 40K decay deposits, on average, 1.0 MeV of energy into the body. What yearly dose in Gy does the typical person receive from the decay of 40K in the body?
Answer:
0.03143 Gy
Explanation:
Mass of the human body = 70 kg
Mass of potassium in the human body = 140 g
chemical atomic mass of potassium = 39.1
From avogadros number, we know that 1 atomic mass of an element contains 6.023 × 10^(23) atoms
Thus,
140g of potassium will contain;
(140 × 6.023 × 10^(23))/(39.1) = 2.1566 × 10^(24) atoms
We are told that the natural abundance of one of the 40K isotopes is 0.012%.
Thus;
Number of atoms of this isotope = 0.012% × 6.023 × 10^(23) = 7.2276 × 10^(19) K-40 atoms
Formula for activity of K-40 is given as;
Activity = (0.693 × number of K-40 atoms)/half life
Activity = (0.693 × 7.2276 × 10^(19))/1300000000
Activity = 3.85 × 10^(10)
We are told that each decay deposits 1.0 MeV of energy into the body.
Thus;
Total energy absorbed by the body in a year = 3.85 × 10^(10) × 1 × 365 = 1405.25 × 10^(10) MeV
Now, 1 MeV = 1.602 × 10^(-13) joules
Thus;
Total energy absorbed by the body in a year = 1405.25 × 10^(10) × 1.602 × 10^(-13) = 2.25 J
1 Gy = 1 J/kg
Thus;
Yearly dose = 2.25/70 = 0.03143 Gy
an electron travels at 0.3037 times the speed of light through a magnetic field and feels a force of 1.2498 pN. What is the magnetic field in teslas
Answer:
Explanation:
Charge on an electron (q) = 1.6 * 10 ^ -19 C
Velocity of electron (v) = 0.3037 * 300,000,000 = 91,110,000 m/sec
We know that, Force exerted on moving particle moving through a magnetic field :
[tex]F= q * v * B ( q,v\ and\ B\ are\ mutually\ perpendicular)[/tex]
1.2498 * 10 ^ -12 = 1.6 * 10^ -19 * 91110000 * B
B = 0.08573 T
The switch on the electromagnet, initially open, is closed. What is the direction of the induced current in the wire loop (as seen from the left)?
Answer:
The induced current is clockwise
What is the threshold velocity vthreshold(ethanol) for creating Cherenkov light from a charged particle as it travels through ethanol (which has an index of refraction of n
Explanation:
The velocity of light in a medium of refractive index [tex]n[tex] is given by,
[tex]v=\frac{c}{n}[/tex]
[tex]v \text { is the velocity of light in the medium }[/tex]
[tex]c \text { is speed of light in vacuum }[/tex]
The exact value of speed of light in vacuum is [tex]299792458 \mathrm{m} / \mathrm{s}[/tex].
For Cherenkov radiation to be emitted, the velocity of the charged particle traversing the medium must be greater than this velocity. Thus, the threshold velocity of for creating Cherenkov radiation is,
[tex]v_{\text {Cherenkov }} \geq \frac{c}{n}[/tex]
[tex]v_{\text {threshod }}=\frac{c}{n}[/tex]
For water [tex]n=1.33,[tex] thus the threshold velocity for producing Cherenkov radiation in water is,
[tex]v_{\text {threatold }(\text { water })} &=\frac{299792458 \mathrm{m} / \mathrm{s}}{1.33}[/tex]
[tex]=225407863 \mathrm{m} / \mathrm{s}[/tex]
[tex]=2.254 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]
For ethanol [tex]n=1.36[tex], thus the threshold velocity for producing Cherenkov radiation in water is,
[tex]v_{\text {threstold }( \text { ettanol) } } &=\frac{299792458 \mathrm{m} / \mathrm{s}}{1.36}[/tex]
[tex]=220435630 \mathrm{m} / \mathrm{s}[/tex]
[tex]=2.204 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]
Answer:
The answer is "2.2 × [tex]\bold{10^8}[/tex]".
Explanation:
In the given question the value of n is missing which can be defined as follows:
n= 1.36
The velocity value of the threshold(ethanol) for a generation the Cerenkov light from the charged particle by travel through ethanol as:
know we will have to use an equation as follows:
Formula:
(ethanol) or the vthreshold = [tex]\frac{c}{n}[/tex]
[tex]= \frac{3\times 10^8} {1.36} \\\\= 2.2 \times 10^8[/tex]
The water in vthreshold:
[tex]= 2.2 \times 10^8 \ \ \frac{m}{ s} \\\\[/tex]
Express the value in c, that is multiple, so, the value of vthreshold(water) is:
=(0.735) c
Positive charge Q is placed on a conducting spherical shell with inner radius R1 and outer radius R2. The electric field at a point r < R1 is:
Answer:
E = 0 r <R₁
Explanation:
If we use Gauss's law
Ф = ∫ E. dA = [tex]q_{int}[/tex] / ε₀
in this case the charge is distributed throughout the spherical shell and as we are asked for the field for a radius smaller than the radius of the spherical shell, therefore, THERE ARE NO CHARGES INSIDE this surface.
Consequently by Gauss's law the electric field is ZERO
E = 0 r <R₁
How long will it take a spacecraft travelling at 99% the speed of light (gamma = 7) to reach
the star Sirius which is 8.6 light-years away according to people on Earth ? How long will it
take according to the crew of the ship?
Answer:
The time taken is [tex]t = 2.739 *10^{8} \ s[/tex]
Explanation:
From the question we are told that
The speed of the spacecraft is [tex]v = 0.99c[/tex]
where c is the speed of light with value [tex]c = 3.0*10^{8} \ m/s[/tex]
=> [tex]v = 0.99 * 3.0 *10^{8 } = 2.97*10^{8}\ m/s[/tex]
The distance of Sirius is [tex]d = 8.6 \ light-years = 8.6 * 9.461*10^{15}= 8.135*10^{16} \ m[/tex]
Generally the time taken is mathematically represented as
[tex]t = \frac{d}{v}[/tex]
substituting values
[tex]t = \frac{8.136 *10^{16}}{2.97 *10^{8}}[/tex]
[tex]t = 2.739 *10^{8} \ s[/tex]
What do we call a substance in
which two or more elements are
chemically bonded
Answer:
A compound
Explanation:
A compound is a substance formed when two or more elements are chemically joined
Answer:
Compound
Explanation:
A compound is a substance derived from the chemical combination of two or more elements
e.g Water ;
= [tex]H_2O\\Hydrogen\:and\:Oxygen[/tex]
Salt ;
[tex]NaCl\\Sodium\:and\: Chlorine[/tex]
Calculate the answers to the appropriate number of significant
12.21 x 9.19 =
A sphere of radius R has charge Q. The electric field strength at distance r > R is Ei.
What is the ratio Ef /Ei of the final to initial electric field strengths if (a) Q is halved, (b) R is halved, and (c) r is halved (but is still > R)? Each part changes only one quantity; the other quantities have their initial values.
Answer:
A. Ef/ Ei = 1/2
B. EF/ Ei = 1
C Ef / Ei = 4
Explanation:
To solve this we apply Coulomb's law which States that
E = Kq / r^2
Where
q = charge r = straight line distance from q to the point in question and
K = Coulomb's constant
Then
Ei = K Q / r^2
So
A) If Q is halved then
Ef = K Q / (2 r^2)
Ef/Ei = 1/2
B) If R is halved, the value of the E-f
at a distance r remains unchanged. So
Ef/Ei = 1
C) if r is now r/2 then
Ef = K Q / (r/2)^2 = K Q / r^2/4 = 4 K Q / r^2
Ef / Ei = 4
please help !!!!!!!!!!!!!!!!!! give the answer to the question i. which lighthouse will be warmer during the day time and why ? ii. which lighthouse will be warmer during the night time and why ? please help
Answer:
I. light house 1 will be warmer during the day ii. light house 2 will be warmer at night.
Explanation:
Because the land conducts heat better than water the light house farthest away from the water will get hotter during as the ground will heat up faster than the water. But this also means that the ground will lose heat faster at night where the water won't making the light house closest to the water hotter at night.
A single-turn current loop carrying a 4.00 A current, is in the shape of a right-angle triangle with sides of 50.0 cm, 120 cm, and 130 cm. The loop is in a uniform magnetic field of magnitude 75.0 mT whose direction is parallel to the current in the 130 cm side of the loop. What is the magnitude of the magnetic force on the
Given that,
Current = 4 A
Sides of triangle = 50.0 cm, 120 cm and 130 cm
Magnetic field = 75.0 mT
Distance = 130 cm
We need to calculate the angle α
Using cosine law
[tex]120^2=130^2+50^2-2\times130\times50\cos\alpha[/tex]
[tex]\cos\alpha=\dfrac{120^2-130^2-50^2}{2\times130\times50}[/tex]
[tex]\alpha=\cos^{-1}(0.3846)[/tex]
[tex]\alpha=67.38^{\circ}[/tex]
We need to calculate the angle β
Using cosine law
[tex]50^2=130^2+120^2-2\times130\times120\cos\beta[/tex]
[tex]\cos\beta=\dfrac{50^2-130^2-120^2}{2\times130\times120}[/tex]
[tex]\beta=\cos^{-1}(0.923)[/tex]
[tex]\beta=22.63^{\circ}[/tex]
We need to calculate the force on 130 cm side
Using formula of force
[tex]F_{130}=ILB\sin\theta[/tex]
[tex]F_{130}=4\times130\times10^{-2}\times75\times10^{-3}\sin0[/tex]
[tex]F_{130}=0[/tex]
We need to calculate the force on 120 cm side
Using formula of force
[tex]F_{120}=ILB\sin\beta[/tex]
[tex]F_{120}=4\times120\times10^{-2}\times75\times10^{-3}\sin22.63[/tex]
[tex]F_{120}=0.1385\ N[/tex]
The direction of force is out of page.
We need to calculate the force on 50 cm side
Using formula of force
[tex]F_{50}=ILB\sin\alpha[/tex]
[tex]F_{50}=4\times50\times10^{-2}\times75\times10^{-3}\sin67.38[/tex]
[tex]F_{50}=0.1385\ N[/tex]
The direction of force is into page.
Hence, The magnitude of the magnetic force on each of the three sides of the loop are 0 N, 0.1385 N and 0.1385 N.
a. The magnitude of the magnetic force on the 130 cm side is 0 Newton.
b. The magnitude of the magnetic force on the 120 cm side is 0.1385 Newton.
c. The magnitude of the magnetic force on the 50 cm side is 0.1385 Newton.
Given the following data:
Current = 4.00 Amperes.Magnetic field strength = 75.0 mT = [tex]7.5 \times 20^{-3}\;T[/tex]Length = 130 cm to m = 1.3 mHypotenuse = 130 cmOpposite side = 120 cmAdjacent side = 50 cmLet us assume the current is flowing in a counterclockwise direction in the right-angle triangle.
First of all, we would determine the angles by using cosine rule:
[tex]C^2=A^2 +B^2 - 2ABCos\alpha \\\\120^2=130^2 +50^2 - 2(130)(50)Cos\alpha\\\\14400 = 16900 + 2500 -13000Cos\alpha\\\\13000Cos\alpha=19400-14400 \\\\Cos\alpha=\frac{5000}{13000} \\\\\alpha = Cos^{-1}(0.3846)\\\\\alpha =67.38^\circ[/tex]
[tex]C^2=A^2 +B^2 - 2ABCos\beta \\\\50^2=120^2 +130^2 - 2(120)(130)Cos\beta \\\\2500 = 14400 + 16900 -31200Cos\beta\\\\31200Cos\alpha=31300-2500 \\\\Cos\beta=\frac{28800}{31200} \\\\\beta = Cos^{-1}(0.9231)\\\\\beta =22.62^\circ[/tex]
a. To the determine the magnitude of the magnetic force on the 130 cm side:
Mathematically, the force acting on a current in a magnetic field is given by the formula:
[tex]F = BILsin\theta[/tex]
Where:
B is the magnetic field strength.I is the current flowing through a conductor.L is the length of conductor.[tex]\theta[/tex] is the angle between a conductor and the magnetic field.Substituting the given parameters into the formula, we have;
[tex]F_{130}=7.5 \times 20^{-3}\times 4 \times 1.3 \times sin(0)\\\\F_{130}=7.5 \times 20^{-3}\times 4 \times 1.3 \times0\\\\F_{130}=0\;Newton[/tex]
b. To the determine the magnitude of the magnetic force on the 120 cm side:
[tex]F_{120}=BILsin\beta[/tex]
[tex]F_{120}=7.5 \times 20^{-3}\times 4 \times 1.2 \times sin(22.62)\\\\F_{120}=7.5 \times 20^{-3}\times 4 \times 1.2 \times0.3846\\\\F_{120}=0.1385\;Newton[/tex]
c. To the determine the magnitude of the magnetic force on the 50 cm side:
[tex]F_{50}=BILsin\alpha[/tex]
[tex]F_{50}=7.5 \times 20^{-3}\times 4 \times 0.5 \times sin(67.38)\\\\F_{50}=7.5 \times 20^{-3}\times 4 \times 1.2 \times0.9231\\\\F_{50}=0.1385\;Newton[/tex]
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Magnetic resonance imaging needs a magnetic field strength of 1.5 T. The solenoid is 1.8 m long and 75 cm in diameter. It is tightly wound with a single layer of 1.50-mm-diameter superconducting wire.
What current is needed?
Answer:
The current needed is 1790.26 A
Explanation:
Given;
magnitude of magnetic field, B = 1.5 T
length of the solenoid, L = 1.8 m
diameter of the solenoid, d = 75 cm = 0.75 m
The magnetic field is given by;
[tex]B = \frac{\mu_o NI }{L}[/tex]
Where;
μ₀ is permeability of free space = 4π x 10⁻⁷ m/A
I is current in the solenoid
N is the number of turns, calculated as;
[tex]N = \frac{Length \ of\ solenoid}{diameter \ of \ wire} \\\\N = \frac{1.8}{1.5*10^{-3}} =1200 \ turns[/tex]
The current needed is calculated as;
[tex]I = \frac{BL}{\mu_o N} \\\\I = \frac{1.5 *1.8}{4\pi *10^{-7} *1200} \\\\I = 1790.26 \ A[/tex]
Therefore, the current needed is 1790.26 A.
Answer:
I = 1790.5 A
Explanation:
The magnetic field due to a solenoid is given by the following formula:
B = μ₀NI/L
where,
B = Magnetic Field Required = 1.5 T
μ₀ = 4π x 10⁻⁷ T/A.m
L = length of Solenoid = 1.8 m
I = Current needed = ?
N = No. of turns = L/diameter of wire = 1.8 m/1.5 x 10⁻³ m = 1200
Therefore,
1.5 T = (4π x 10⁻⁷ T/A.m)(1200)(I)/1.8 m
I = (1.5 T)(1.8 m)/(1200)(4π x 10⁻⁷ T/A.m)
I = 1790.5 A
A 10-cm-long thin glass rod uniformly charged to 6.00 nC and a 10-cm-long thin plastic rod uniformly charged to - 6.00 nC are placed side by side, 4.4 cm apart. What are the electric field strengths E1 to E3 at distances 1.0 cm, 2.0 cm, and 3.0 cm from the glass rod along the line connecting the midpoints of the two rods?
A. Specify the electric field strength E1
B. Specify the electric field strength E2
C. Specify the electric field strength E3
Answer:
A) E(r) = 1.3957 × 10^(5) N/C
B) E(r) = 9.8864 × 10⁴ N/C
C) E(r) = 1.13 × 10^(5) N/C
Explanation:
We are given;
q = 6 nc = 6 × 10^(-9) C
L = 10 cm = 0.1 m
d = 4.4 cm = 0.044 m
r1 = 1 cm = 0.01 m
r2 = 2 cm = 0.02 m
r3 = 3 cm = 0.03 m
Formula for the electric field strength in this question is given as;
E(r) = q/(2π(ε_o)rL) + q/(2π(ε_o)(d - r)L)
When factorized, we have;
E(r) = q/(2π(ε_o)L) × [(1/r) + (1/(d - r))]
Plugging in the relevant values for q/(2π(ε_o)L)
We know that (ε_o) has a constant value of 8.854 × 10^(−12) C²/N².m
Thus; q/(2π(ε_o)L) = (6 × 10^(-9))/(2π(8.854 × 10^(−12)0.1) = 1078.53
Thus;
E(r) = 1078.52 [1/r + 1/(d - r)]
A) E1 is at r = 1 cm = 0.01m
Thus;
E(r) = 1078.52 (1/0.01 + (1/(0.044 - 0.01))
E(r) = 1.3957 × 10^(5) N/C
B) E2 is at r = 2 cm = 0.02 m
Thus;
E(r) = 1078.52 (1/0.02 + (1/(0.044 - 0.02))
E(r) = 9.8864 × 10⁴ N/C
C) E2 is at r = 3 cm = 0.03 m
Thus;
E(r) = 1078.52 (1/0.03 + (1/(0.044 - 0.03))
E(r) = 1.13 × 10^(5) N/C
Water flows through a cylindrical pipe of varying cross-section. The velocity is 5.00 m/s at a point where the pipe diameter is 1.50 cm. At a point where the pipe diameter is 3.00 cm, the velocity is
Explanation:
We know that rate of flow through a cross section :
[tex]v1 \times a1 = v2 \times a2[/tex]
5 m/s * 1.76cm^2 = v2 * 7.06cm^2
[tex]v2 = 1.24 \: m {s}^{ - 1} [/tex]
At a point where the pipe diameter is 3.00 cm, the velocity is 1.25 m/s.
What is fluid flow?Fluid Flow, a branch of fluid dynamics, is concerned with fluids. It involves the movement of a fluid under the influence of uneven forces. As long as unbalanced pressures are applied, this motion will persist.
Given parameters:
Initial velocity of the water: u = 5.00 m/s
Initial diameter of the pipe: d = 1.50 cm.
Final diameter of the pipe: D = 3.00 cm.
Final velocity of the water: v = ?
In fluid motion:
velocity×(diameter)² = constant
Hence, initial velocity × ( initial diameter)² = final velocity × ( final diameter)²
ud² = vD²
v = u (d/D)²
v= 5 × (1.50/3.0)²
v= 5/2²
v= 5/4
v= 1.25 m/s.
Hence, at a point where the pipe diameter is 3.00 cm, the velocity is 1.25 m/s.
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