Question

A closed loop conductor that forms a circle with a radius of 1.8 m is located in a uniform but changing magnetic field. If the maximum emf induced in the loop is 9.0 V, what is the maximum rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop lies

Answer 1

Answer:

The maximum rate at which the magnetic field strength is changing is 0.88 T/s.

Explanation:

Given that,

Radius of the closed loop conductor that forms a circle, r = 1.8 m is located in a uniform but changing magnetic field.

The maximum emf induced in the loop is 9 volt.

We need to find the maximum rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop. The induced emf is given by :

$\epsilon=-\dfrac{d\phi}{dt}$

$\phi=BA$

$\epsilon=-\dfrac{d(BA)}{dt}\\\\\epsilon=A\times \dfrac{dB}{dt}\\\\\dfrac{dB}{dt}=\dfrac{\epsilon}{A}\\\\\dfrac{dB}{dt}=\dfrac{9}{\pi (1.8)^2}\\\\\dfrac{dB}{dt}=0.88\ T/s$

The maximum rate at which the magnetic field strength is changing is 0.88 T/s. Hence, this is the required solution.