Question

A circle with a radius of 0.3 meters is placed in the x-y plane in a magnetic field directed in the -z direction. It is wound once and its resistance is 8 Ohms. The initial magnetic field is 0.5 Tesla. The magnetic field is then changed in 0.7 s and the average induced current is 0.05 amps running counter-clockwise. First, find the final magnetic field to needed to induce this average current.

Then, the magnetic field (still in the -z direction) is held constant at the value of the final magnetic field that was just found. Then, the wire is reshaped into a square that is wound once in a time of 0.003 seconds. If the resistance does not change, what is the average induced current, in amps, when the wire changes shape? If it's clockwise include a negative sign.

Answer 1

The expression for induced current is

where i is the induced current

A is the area normal to the magnetic field

R is the resistance in the circuit

B is the magnetic field and t is the time

As we are dealing with coil and magnetic field is perpendicular to the coil

0.28 m2

where r is the radius of the coil

Now using this value and the values given in the problem we have and using the first expression

which gives

as initial magnetic field was 0.5 T

gives

where Bf  is the final magnetic field. (unlike given in the question the magnetic field has changed sign, check if the question is correct).

For the second part the magnetic field is not changing its' value, but the area is changing. It can also induce a magnetic field

The wire is not being cut and simply reshaped so the perimeters of the shapes will be same irrespective of the shape.

Hence,

where a is the length of the square

so we get the area of the square in terms of the radius of the given circle to be

so the change in the area from circle to square is

using the values given we have

it is not negative.