Question

In a coil of resistance \(150\,\Omega\), a current is induced by changing the magnetic flux through it as shown by figure. The magnitude of flux through the coil is \( \_\_\_ \, \text{Wb} \).

Hint:

Flux change = Resistance × Area under \(I\)-\(t\) graph.

Answer 1

Step 1: Understanding the Concept:
According to Faraday's Law of Electromagnetic Induction, the induced EMF is equal to the rate of change of magnetic flux. Since current is induced in a closed circuit with resistance, we can relate the total charge flow to the total change in flux.
Step 2: Key Formula or Approach:
1. Induced current: \( i = \frac{e}{R} = \frac{1}{R} \left| \frac{d\phi}{dt} \right| \).
2. Integrating both sides with respect to time: \( \int i \, dt = \frac{1}{R} \int d\phi \).
3. Total charge \( q = \frac{\Delta \phi}{R} \).
4. Change in flux: \( \Delta \phi = R \times q \), where \( q \) is the area under the current-time graph.
Step 3: Detailed Explanation:
From the given current-time graph, the current starts at 10 A and drops linearly to 0 A over a period of 0.4 s.
The total charge \( q \) is the area of the triangle:
\[ q = \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ q = \frac{1}{2} \times 0.4 \text{ s} \times 10 \text{ A} = 2 \text{ C} \]
Given resistance \( R = 150 \, \Omega \).
The change in magnetic flux is:
\[ \Delta \phi = R \times q \]
\[ \Delta \phi = 150 \, \Omega \times 2 \text{ C} = 300 \text{ Wb} \]
Step 4: Final Answer:
The magnitude of the change in flux is 300 Wb.