Question

A small circular loop of area 2.20 cm2 is placed in the plane of, and concentric...

A small circular loop of area 2.20 cm2 is placed in the plane of, and concentric with, a large circular loop of radius 1.23 m. The current in the large loop is changed at a constant rate from 219 A to -219 A (a change in direction) in a time of 1.14 s, starting at t = 0.What is the magnitude of the magnetic field at the center of the small loop due to the current in the large loop at (a) t = 0, (b) t = 0.570 s, and (c) t = 1.14 s? (d) From t = 0 to t = 1.14 s, is B reversed? Because the inner loop is small, assume is uniform over its area. (e) What emf is induced in the small loop at t = 0.570 s?

Homework Answers

Answer #1

given

dI/dt = (-219-219)/1.14 = -384.2

dI = -384.2*dt

I = integral dI

I = Io - 384.2*t


Io = 219 A

I = 219 - 384.2*t


magnetic field B due to large loop B = uo*I/(2R)


part(a)


at t = 0


I = 219

B = 4*pi*10^-7*219/(2*1.23)


B = 1.1*10^-4 T


part(b)

at t = 0.57 s

I = 219 - (384.2*0.57) = 0.006 A

B = 4*pi*10^-7*0/(2*1.23)

B = 0

part(c)


at t = 1.14 s

I = 219 - 384.2*1.14 = -219 A


B = -4*pi*10^-7*219/(2*1.23)


B = -1.1*10^-4 T


B is reversed


part(d)

flux = B*A = uo*I*A/(2R) = ( A*uo/2R)*(Io - 384.2*t)


EMF = -(d/dt)*flux


EMF = ( A*uo/2R)*384.2

emf = 2.2*10^-4*4pi*10^-7*384.2/(2*1.23)


emf = 4.32*10^-8 T

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A small circular loop of area 2.34 cm2 is placed in the plane of, and concentric...
A small circular loop of area 2.34 cm2 is placed in the plane of, and concentric with, a large circular loop of radius 1.22 m. The current in the large loop is changed at a constant rate from 203 A to -203 A (a change in direction) in a time of 1.17 s, starting at t = 0.What is the magnitude of the magnetic field at the center of the small loop due to the current in the large loop...
A circular loop of wire with an area of .1m^2 is placed in a 2T magnetic...
A circular loop of wire with an area of .1m^2 is placed in a 2T magnetic field. The field increases at a rate of 0.2 T/S. What is the induced emf in the loop? What is the direction of the induced current in the loop?
A circular loop of wire of area 0.25?2 lies in the x-y plane with its center...
A circular loop of wire of area 0.25?2 lies in the x-y plane with its center at the origin. A uniform magnetic field of 2.00 T points in the positive z-direction. The loop begins to rotate at t = 0s at the rate of 60 rpm. a. What is the flux through the loop as a function of time? b. What is the emf in the loop as a function of time? c. If the loop has a resistance of...
A circular loop in the plane of the paper lies in a 0.75 T magnetic field...
A circular loop in the plane of the paper lies in a 0.75 T magnetic field pointing into the paper. The loop’s diameter is changed from 20.0 cm to 6.0 cm in 0.50 s. Determine the direction of the induced current and justify your answer. Determine the magnitude of the average induced emf. If the coil resistance is 2.5 Ω, what is the average induced current?
A single loop of aluminum wire, lying flat in a plane, has an area of 8.00...
A single loop of aluminum wire, lying flat in a plane, has an area of 8.00 cm2 and a resistance of 2.50 Ω. A uniform magnetic field points perpendicular to the plane of the loop. The field initially has a magnitude of 0.500 T, and the magnitude increases linearly to 2.00 T in a time of 2.00 s. What is the induced current (in mA) in the loop of wire over this time?
A circular loop in the plane of the paper lies in a 0.76 T magnetic field...
A circular loop in the plane of the paper lies in a 0.76 T magnetic field pointing into the paper. If the loop's diameter changes from 20.2 cm to 9.6 cm in 0.56 s. What is the direction of the induced current? What is the magnitude of the average induced emf?
A circular loop in the plane of the paper lies in a 0.38 T magnetic field...
A circular loop in the plane of the paper lies in a 0.38 T magnetic field pointing into the paper. Part A: If the loop's diameter changes from 19.4 cm to 5.8 cm in 0.49 s , what is the direction of the induced current? Part B: What is the magnitude of the average induced emf?
A time-varying magnetic field is perpendicular to the plane of a circular loop of diameter 10...
A time-varying magnetic field is perpendicular to the plane of a circular loop of diameter 10 cm made with wire of diameter 3.4 mm and resistivity 2.07 × 10-8?·m. The magnetic field increases as a function of time, with magnitude B = (0.79 t) T/s a) What is the magnitude of the emf induced in the loop? b) What is the value of the current through the loop? c) At what rate does energy appear as thermal energy in the...
A circular loop in the plane of the paper lies in a 0.78 T magnetic field...
A circular loop in the plane of the paper lies in a 0.78 T magnetic field pointing into the paper. A) What is the magnitude of the average induced emf? Answer in V. B) If the coil resistance is 4.3 ohm , what is the average induced current? Answer in A
E16M.8 Two concentric circular coils lie on a tabletop. The outer coil has a radius r0...
E16M.8 Two concentric circular coils lie on a tabletop. The outer coil has a radius r0 = 25 cm, consists of N = 100 turns of wire, and conducts a sinusoidal 60-Hz alternating current with a maximum value of i0 = 5.0 A. The inner coil is much smaller, with a radius of r = 1.0 cm. It has a single turn (and so is just a loop) with a resistance of R = 0.01 Ω. A)What approximations do we...