Question

(b) 0.25 mV, 92.6 ?A, (c) 4.63 ?N

STOP TO THINKA conducting loop is halfway into a magnetic field. Suppose the magnetic field begins to increase rapidly in strength. - What happens to the loop? This problem is based on an example from a textbook Assume that the loop dimensions are 10 5 cm, ??/Ar-0.1 T/s, and the loop resistance is 2.7 ? (a) What is the direction of the current in the loop? (Explain your reasoning.) (b) Find the EMF and the current in the loop. (c) Find the magnitude and direction of the force which is exerted on the loop when B-1T. (d) How would your answers to (c) change in the following circumstances? (Explain carefully.) (i) The loop is completely inside the field region. (ii) The loop is completely outside the field region. (iii) Only one-fourth of the loop is within the field region

Answer 1

length,l=10cm

breadth, b=5cm

dB/dt=0.1 T/sec

resistance,R=2.7 ohms

a)

here,

the magnetic flux increases,

now according to Lenz's law,

the induced current will produce the magnetci field which try to decreases the flux,

hence, the direction of current should be anticlockwise.

b)

emf=A*dB/dt

=(l/2*b)*dB/dt

=(10/2*5)*10^-4*0.1

=2.5*10^-4 v

current,I=emf/R

=2.5*10^-4/(2.7)

=9.26*10^-5 A

c)

if B=1T

the only force acts on the leftside of the loop,

F=I*b*B

F=9.26*10^-5*5*10^-2*1

F=4.63*10^-6 T (direction of the force is towards the right)

d)

(i)

Fnet=0

because,

the force created by the current on the upper part gets cancelled due to lower part

similarly force on the left side part gets cancelled due to rigtside,

(ii)

Fnet =0

if the loop is completely outside the field region, then there is no change in flux

and the induced emf is zero therefore Fnet is also zero

(iii)

the force created by the current on the upper part gets cancelled due to lower part

and the only force acts on the loop which is along leftside,