Ncert Exercises & Solutions

A magnetic field in a certain region is given by $B = B_{0} \cos (ω t) \hat{k}$ and a coil of radius a with resistance R is placed in the x-y plane with its centre at the origin in the magnetic field (figure). Find the magnitude and the direction of the current at (a, 0, 0) at

Hint: The current in the coil depends on the rate of change of magnetic flux.

Step 1: At any instant, flux passes through the ring is given by;

ϕ = B . A = BAcosθ = BA (∵ θ = 0)

or ϕ = B_{0} ({πa}^{2}) \cos ωt

By Faraday's law of electromagnetic induction,

The magnitude of induced emf is given by;

ε = |- \frac{dϕ}{dt}| = B_{0} ({πa}^{2}) ωsinωt

This causes the flow of induced current, which is given by;

I = B_{0} ({πa}^{2}) ωsinωt / R

Step 2: Now, finding the value of current at different instants, so we have current at:

t = \frac{π}{2 ω}

I = \frac{B_{0} ({πa}^{2}) ω}{R}

along

\hat{j}

Because

sinωt = \sin (ω \times \frac{π}{2 ω}) = \sin \frac{π}{2} = 1

At t = \frac{π}{ω}, I = \frac{B ({πa}^{2}) ω}{R} sinπ = 0

Here,

sinωt = \sin (ω \times \frac{π}{ω}) = sinπ = 0

t = \frac{3}{2} \frac{π}{ω}

I = \frac{B ({πa}^{2}) ω}{R} along - \hat{j}

sinωt = \sin (ω \times \frac{3 π}{2 ω}) = \sin \frac{3 π}{2} = - 1

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions