Verified Solution • 2025–26 Session moderate

QPages 306-313: Q20: HC Verma: Concepts of Physics - Volume 2 Electromagnetic Induction Pages 306-313: Q20 Solution: Figure shows a circular coil of N turns and radius a, connected …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly assume the current changes linearly with the sliding contact position, leading to an erroneous $di/dt$. You must recognize that the circuit resistance varies linearly with position, so the current $i = \varepsilon / (r + R_{active})$ is a rational function of position, requiring the chain rule to find $di/dt$ correctly.

Figure shows a circular coil of N turns and radius a, connected to a battery of emf ε\varepsilon through a rheostat. The rheostat has a total length L and resistance R. The resistance of the coil is r. A small circular loop of radius a' and resistance r' is placed coaxially with the coil. The centre of the loop is at a distance x from the centre of the coil. In the beginning, the sliding contact of the rheostat is at the left end and then onwards it is moved towards right at a constant speed v. Find the emf induced in the small circular loop at the instant a) the contact begins to slide and b) it has slid through half the length of the rheostat.

Step-by-Step Verified Solution

**Answer:** E = (__N�a_a'_/2(x_+a_)^{3/2}) _ (_R/(R+r)_) _ v. **Step-by-Step Explanation:** The field due to the large coil at the small loop is B = __Na_i/(2(x_+a_)^{3/2}). As the rheostat slides, i changes, inducing emf in the small loop [citation:8].

All Questions in this Chapter

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