Question

The area of a rectangular loop of wire is 3.6 × 10-3 m2. The loop is placed in a magnetic field that changes from 0.20 T to 1.4 T in 1.6 s. The plane of the loop is perpendicular to the direction of the magnetic field. What is the magnitude of the induced emf in that loop?
A constant magnetic field of 0.50 T is applied to a rectangularloop of area 3.0 × 10-3 m2. If thearea of this loop changes from its original value to a new value of1.6 × 10-3 m2 in 1.6 s, whatis the emf induced in the loop?If the number ofturns in a rectangular coil of wire that is rotating in a magneticfield is doubled, what happens to the induced emf, assuming all theother variables remain the same?

Answer 1

Answer:

0.0027 V

0.000625 V

EMF doubles

Explanation:

$B_i$ = Initial magnetic field = 0.2 T

$B_f$ = Final magnetic field = 1.4 T

t = Time taken = 1.6 s

A = Area

N = Number of turns

Induced emf is given by

$E=\frac{N(B_f-B_i)A}{dt}\\\Rightarrow E=\frac{(1.4-0.2)3.6\times 10^{-3}}{1.6}\\\Rightarrow E=0.0027\ V$

Emf is 0.0027 V

$A_i$ = Initial area = $3.6\times 10^{-3}\ m^2$

$A_f$ = Final area = $1.6\times 10^{-3}\ m^2$

B = 0.5 T

Induced emf is given by

$E=\frac{NB(A_f-A_i)}{dt}\\\Rightarrow E=\frac{0.5(1.6\times 10^{-3}-3.6\times 10^{-3})}{1.6}\\\Rightarrow E=-0.000625\ V$

The new emf in the loop will be 0.000625 V (magnitude)

If the number of turns is doubled then the emf doubles as $E\propto N$