Verified Solution • 2025–26 Session moderate

QPages 306-313: Q48: HC Verma: Concepts of Physics - Volume 2 Electromagnetic Induction Pages 306-313: Q48 Solution: The rectangular wire-frame, shown in figure, has a width d,…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently assign the wrong sign to the magnetic drag force, treating it as additive rather than opposing the applied force $F$. Remember that the induced current creates a magnetic force $F_B = \frac{B^2 d^2 v}{R}$ that always opposes the motion (Lenz's Law), so the net force equation must be $F - \frac{B^2 d^2 v}{R} = ma$.

The rectangular wire-frame, shown in figure, has a width d, mass m, resistance R and a large length. A uniform magnetic field B exists to the left of the frame. A constant force F starts pushing the frame into the magnetic field at t = 0. a) Find the acceleration of the frame when its speed has increased to v. b) Show that after some time the frame will move with a constant velocity till the whole frame enters into the magnetic field. Find this velocity v0v_0. c) Show that the velocity at time t is given by v=v01−e−Ft/mv0)v = v_01 - e^{-Ft/mv_0}).

Step-by-Step Verified Solution

**Answer:** (a) a = (RF - B_d_v)/(mR) (b) v_ = FR/(B_d_) (c) v = v_(1 - e^(-Ft/mv_)). **Step-by-Step Explanation:** (a) Net force = F - B_d_v/R. a = F_net/m. (b) At constant velocity, F = B_d_v_/R. (c) Solving the differential equation gives the exponential approach [citation:16].

All Questions in this Chapter

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