A constant uniform magnetic field of 0.50 T is applied at right angles to the plane of a flat rectangular loop of area 3.0 × $10 ^{- 3}$ $m ^ { 2 }$ . If the area of this loop changes steadily from its original value to a new value of 1.6 × 10^-3 m² in 1.6 s, what is the emf induced in the loop? A) 1.6 × $10^{ - 2}$ V B) 0 V C) 7.5 × $10 ^{- 2}$ V D) 4.4 × $10 ^{- 4}$ V E) 9.0 × $10 ^{- 2}$ V

Question

Quizplus · Accepted Answer

The emf induced in a coil is given by

$emf = - \dfrac{d\phi}{dt}$,

where $\phi$ is the flux through the coil. The flux through the coil in a uniform magnetic field is given by $\phi = BA$, where $B$ is the magnetic field and $A$ is the area of the loop.

As the area of the loop changes, the flux through the loop changes. The rate of change of the area is given as:

$\dfrac{dA}{dt} = \dfrac{(1.6 	imes 10^{-3} - 3.0 	imes 10^{-3})}{1.6} = -1.25 	imes 10^{-3}m^2/s$

The emf induced in the loop is:

$emf = - \dfrac{d\phi}{dt} = -\dfrac{d(BA)}{dt} = -B\dfrac{dA}{dt}$

Substituting the values, we get:

$emf = - (0.50 T) 	imes (-1.25 	imes 10^{-3}m^2/s) = 4.4 	imes 10^{-4} V$

Therefore, the answer is D) 4.4 × 10^{-4} V.

A Constant Uniform Magnetic Field of 0 10−310 ^{- 3}10−3 m2m ^ { 2 }m2

A Constant Uniform Magnetic Field of 0 $10 ^{- 3}$ $m ^ { 2 }$