Question

A conductor is formed into a loop that encloses an area of 1m^2. The loop is oriented at a angle 30 degree with the xy plane. A varying magnetic field is oriented parallel to the z axis. If the maximum emf induced in the loop is 10v, what is the maximum rate at which the magnetic field strength is changing?

Answer 1

Answer:

$\frac{dB}{dt} = 11.55 T/s$

Explanation:

As we know that flux of magnetic field from the closed loop is given by

$\phi = BAcos30[tex]

now by Faraday's law we know

[tex]EMF = \frac{d\phi}{dt}$

now we will have

$EMF = Acos30\frac{dB}{dt}$

now we have

$A = 1 m^2$

EMF = 10 Volts

$10 = 1 (cos30)\frac{dB}{dt}$

$\frac{dB}{dt} = \frac{20}{\sqrt3}$

$\frac{dB}{dt} = 11.55 T/s$