The area of a rectangular loop of wire is 3.6 × $10 ^{- 3}$ $m ^ { 2 }$ The loop is placed in a uniform $\vec { B }$ field that changes steadily from 0.20 T to 1.4 T in 1.6 s.The plane of the loop is perpendicular to the direction of the $\vec { B }$ field.What is the magnitude of the induced emf in that loop?
A)2.8 × $10 ^{- 3}$ V
B)2.7 × $10 ^{- 3}$ V
C)0 V
D)1.8 × $10^{ - 3}$ V
E)3.0 × $10 ^{- 3}$ V

Question

Quizplus · Accepted Answer

The induced emf in the loop is given by Faraday's Law:

$\varepsilon = -\frac{d\Phi}{dt}$

where $\Phi$ is the magnetic flux through the loop. Since the loop is perpendicular to the magnetic field, the flux is given by:

$\Phi = BA$

where B is the magnetic field and A is the area of the loop.

The change in magnetic field over time is given by:

$\frac{\Delta B}{\Delta t} = \frac{1.4 \mathrm{T} - 0.20 \mathrm{T}}{1.6 \mathrm{s}} = 0.75 \mathrm{T/s}$

Substituting these values into the equation for the induced emf, we get:

$\varepsilon = -\frac{d\Phi}{dt} = -A \frac{dB}{dt} = -(3.6\times 10^{-3} \mathrm{m^2})(0.75 \mathrm{T/s}) = -2.7\times 10^{-3} \mathrm{V}$

Since the negative sign just indicates the direction of the current, the magnitude of the induced emf is 2.7 × 10−3 V. Therefore, the best choice is B.

The Area of a Rectangular Loop of Wire Is 3 10−310 ^{- 3}10−3

The Area of a Rectangular Loop of Wire Is 3 $10 ^{- 3}$