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MHT CET202616 April 2026Morning ShiftPhysicsElectromagnetic InductionActual

A metal rod of length 'L' completes the circuit as shown. The area of the circuit is perpendicular to magnetic field 'B'. Total resistance of the circuit is 'R'. The force needed to move the rod in the direction as shown with constant speed 'V' is

Options

  1. ABVL R
  2. BB ^2 L ^2 V R
  3. CB ^2 L ^2 V ^2 R
  4. DBLV ^2 R

Correct answer

B. B ^2 L ^2 V R

Step-by-step solution

When the metal rod of length L moves with a velocity V perpendicular to a uniform magnetic field B , a motional emf is induced across its ends. The induced emf is given by: E = BVL This emf drives an induced current I through the circuit with total resistance R : I = E R = BVL R The current-carrying rod experiences a magnetic force F_m opposing its motion (due to Lenz's Law), which is given by: F_m = ILB Substituting the value of I into the force equation: F_m = ( BVL R )LB = B^2L^2V R To move the rod with a consta

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