Magnetic Flux and Induced Current – Graph Analysis

Physics – Induced Current from Magnetic Flux vs Time Graph

Question:

Multiple Choice (10 points)

The graph below shows the magnetic flux Φ through a loop over time. Which of the following shows the correct current I through the loop over the same time interval?

Answer and Detailed Explanation:

Step 1: Understand the Graph of Magnetic Flux

The magnetic flux Φ vs time graph has two regions:

Region 1 (0 < t < 3 s): Linear decrease in flux
Region 2 (3 < t < 6 s): Flux is constant

Step 2: Apply Faraday’s Law of Induction

Faraday’s law gives the induced EMF as:
ε = -dΦ/dt

For Region 1:

The flux is decreasing at a constant rate → dΦ/dt = constant < 0
Thus, ε = – (negative value) = positive constant

→ The induced EMF and therefore current is positive and constant.

For Region 2:

Flux is constant → dΦ/dt = 0
Hence, ε = 0

→ No induced current in this region.

Step 3: Use Ohm’s Law to Relate EMF and Current

Ohm’s law: I = ε / R (where R is resistance)
So, current follows the same behavior as EMF:

0 < t < 3 s: Current is positive and constant
3 < t < 6 s: Current is zero

      ✅ Final Answer:

      The current is positive and constant between 0 < t < 3 s  
      and zero between 3 < t < 6 s.

      Correct Option: 5

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