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Question #43314

Difficulty: 8/10 | 🟢 Free

The Question

A uniform time-varying magnetic field $\vec{B} = \alpha t \hat{k}$ (where $\alpha > 0$ is a constant and $t$ is time) exists in a cylindrical region of space of radius $2R$ whose axis coincides with the $z$ -axis. A particle of charge $+q$ is moved from the origin $(0,0,0)$ to the point $(R, R, 0)$ along a parabolic path $y = \frac{x^2}{R}$ in the $xy$ -plane. What is the work done by the induced electric field on the charge during this process?

Options

A.
$-\frac{q\alpha R^2}{6}$
B.
$0$
C.
$\frac{q\alpha R^2}{2}$
D.
$-\frac{q\alpha R^2}{2}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Induced Electric Fields|Variable Force Integration|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between conservative electrostatic fields and non-conservative induced electric fields.

A common trap for JEE Advanced students is to reflexively apply the Work-Energy Theorem using a scalar potential difference ( $W = -q\Delta V$ ).

If a student incorrectly assumes the induced field is conservative, they might integrate the radial field magnitude to find a pseudo-potential, or assume path independence and choose a simpler straight-line path (yielding $0$ ).

By forcing the evaluation over a specific parabolic trajectory, the problem demands direct vector integration of the Lorentz force ( $\vec{F} \cdot d\vec{r}$ ), highlighting that work done by induced fields is strictly path-dependent.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Induction - Class 12
Concept	Induced Electric Fields
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free