Question

A coil of 100 turns experiences a change in magnetic flux from 0.05 Wb to 0.01 Wb in 0.2 s. The induced emf is:

• A. 10 V
• B. 15 V
• C. 20 V
• D. 25 V

Hint:

Remember that the induced emf is directly proportional to the number of turns ($N$).
Do not forget to multiply the rate of change of flux by the number of turns.
A common error is calculating only the single-turn emf ($0.2\text{ V}$) and missing the factor of $100$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question belongs to the topic "Electromagnetic Induction."
We are required to determine the magnitude of the induced electromotive force (emf) in a coil of $100$ turns when the magnetic flux passing through it changes by a given amount in a specified time interval.

Step 2: Key Formula or Approach:
According to Faraday's Law of Electromagnetic Induction, the magnitude of the induced electromotive force ($e$) is given by:
\[ e = N \left| \frac{\Delta \Phi}{\Delta t} \right| \]
where:
$N$ = number of turns of the coil
$\Delta \Phi = \Phi_2 - \Phi_1$ is the change in magnetic flux
$\Delta t$ = time interval during which the change occurs

Step 3: Detailed Explanation:

• We are given the following experimental parameters:
Number of turns ($N$) = $100$
Initial magnetic flux ($\Phi_1$) = $0.05\text{ Wb}$
Final magnetic flux ($\Phi_2$) = $0.01\text{ Wb}$
Time interval ($\Delta t$) = $0.2\text{ s}$

• Calculate the change in magnetic flux ($\Delta \Phi$):
\[ \Delta \Phi = \Phi_2 - \Phi_1 = 0.01\text{ Wb} - 0.05\text{ Wb} = -0.04\text{ Wb} \]

• Taking the absolute value of the change in flux:
\[ |\Delta \Phi| = 0.04\text{ Wb} \]

• Substitute these values into the Faraday's Law formula:
\[ e = 100 \times \frac{0.04\text{ Wb}}{0.2\text{ s}} \]

• Calculate the rate of change of flux:
\[ \frac{0.04}{0.2} = 0.2\text{ Wb/s} \]

• Multiply by the number of turns:
\[ e = 100 \times 0.2\text{ V} = 20\text{ V} \]

• The negative sign in Lenz's law indicates that the direction of the induced emf is such that it would produce a current to oppose the change in magnetic flux.



Step 4: Final Answer:
The induced electromotive force in the coil is $20\text{ V}$, which corresponds to option (C).