Question

A square conducting loop 8.4 cm on a side is placed in a uniform B-field so that the plane of the loop is perpendicular to the direction of the field lines. If the loop is then converted into a rectangular loop measuring 2.1 cm on its shortest side in 6.50 ms, and the average emf induced across the loop is 14.7 V during this time period, what is

A) the strength of the B-field?

B) What is the direction of the induced current in the conducting loop (assume the B-field is directed out of the page, show direction in your picture or with the words “Clockwise” or “Counter-Clockwise”)?

Answer 1

from the given data

initial area of the loop, A1 = Area of the square

= 0.084^2

= 0.007056 m^2

final area of the loop, A2 = area of the rectangle

= 0.021*(0.084 + (0.084 - 0.021))

= 0.021*0.147

= 0.003087 m^2

dt = 6.5 ms = 6.5*10^-3 s
induced emf = 14.7 V

let B is the strength of the magnetic field.

A) we know, induced emf = the rate of change of magnetic flux through the loop

induced emf = B*(A1 - A2)/dt

B = induced emf*dt/(A1 - A2)

= 14.7*6.5*10^-3/(0.007056 - 0.003087)

= 24.1 T <<<<<<------------Answer

B) clockwise

According to Lenz's law the direction of induced emf(or induced current) is always such as to oppose the change in magnetic flux that generated it.