Question 317: Electromagnetic Induction

Question

The magnitude of flux linked with coil varies with time as $$\phi=3 t^2+4 t+7$$. The magnitude of induced e.m.f. at $$t=2 \mathrm{~s}$$ is

Accepted Answer

To find the magnitude of the induced electromotive force (e.m.f.) in the coil, we'll use Faraday's Law of Electromagnetic Induction. Faraday's Law states that the induced e.m.f. in a coil is equal to the negative rate of change of magnetic flux through the coil. Mathematically, this can be expressed as:
$$ 	ext{e.m.f.} = -\frac{d\phi}{dt} $$
Given that the magnetic flux $$\phi$$ varies with time $$t$$ as:
$$ \phi = 3t^2 + 4t + 7 $$
We need to find the derivative of $$\phi$$ with respect to $$t$$ in order to determine the rate of change of the magnetic flux. Differentiating $$\phi$$ with respect to $$t$$, we get:
$$ \frac{d\phi}{dt} = \frac{d}{dt}(3t^2 + 4t + 7) $$
Applying the differentiation rule, we get:
$$ \frac{d\phi}{dt} = 6t + 4 $$
Now, we need to find the induced e.m.f. at $$t = 2 \, 	ext{s}$$. Substitute $$t = 2$$ into the derivative:
$$ \frac{d\phi}{dt} \bigg|_{t=2} = 6(2) + 4 = 12 + 4 = 16 $$
According to Faraday's Law, the induced e.m.f. is the negative of this value. However, since the question asks for the magnitude of the induced e.m.f., we will consider the positive value:
$$ 	ext{Magnitude of induced e.m.f.} = 16 \, 	ext{V} $$
Hence, the correct answer is:
Option B:
16 V

Answer

3 V

Answer

16 V

Answer

10 V

Answer

7 V

Electromagnetic Induction

The magnitude of flux linked with coil varies with time as $\phi=3 t^2+4 t+7. The magnitude of induced e.m.f. at t=2 \mathrm{~s}$ is

Choose the correct answer: