Question

3. (15 points) A circular coil of radius 5 cm has 50 turns of wire. The uniform magnetic field directed into the page/screen (see the figure below) is linearly increased in magnitude form 0 to 0.8 T. What time interval for this increase is needed to induce in the coil emf = 0.25 V? What is the direction of the induced emf (clockwise/conterclockwise)? X X X To solve this problem I used A. The Coulomb's law; B. The Snall's law; C. The Faradey's law; D. The Lentz's law; E. A and B; F. C and D. х B X X X X

Answer 1

Given:

N = 50 turns

r = 5 cm

Change in magnetic field = $\Delta B = 0.8-0=0.8T$

E = e.m.f induced = 0.25 V

According to Faraday's Law, the magnitude of e.m.f induced = $E=\left |\frac{\Delta \phi}{\Delta t} \right |$ , [where $\Delta t$ = time interval, $\phi = BA$ = magnetic flux, when magnetic field is perpendicular to plane of loop]

As only, magnetic field is changed, the expression of magnitude of e.m.f induced is = $E=\left |\frac{\Delta B}{\Delta t} \right |*NA$

Therefore,

$0.25= \frac{0.8}{t}*50*\pi*(5*10^{-2})^{2}$

$\Rightarrow t= \frac{0.8}{0.25}*50*\pi*(5*10^{-2})^{2}=1.26s$.

Therefore, the time interval is t = 1.26 s. [answer]

According to Lenz's Law, As the magnetic field is increasing the flux through the coil is increasing, therefore, to oppose this flux, the magnetic field due to induced current should be out of the plane of figure, and this is possible if the direction of induced current or induced e.m.f is counter-clockwise.

Therefore, the direction of induced e.m.f is counter-clockwise. [answer]

To solve this problem, I have used Faraday's Law and Lenz's Law.

Therefore, the correct option is F. [answer]