JEE Main202324 Jan 2023Evening ShiftPhysicsElectromagnetic InductionActual
A metallic rod of length L is rotated with an angular speed of ω normal to a uniform magnetic field B about an axis passing through one end of rod as shown in figure. The induced emf will be : .
Options
- A1 2 B 2 L 2 ω
- B1 4 B L 2 ω
- C1 2 B L 2 ω
- D1 4 B 2 L ω
Correct answer
C. 1 2 B L 2 ω
Step-by-step solution
Linear velocity at the distance x from the centre can be written as, v = ω x . Therefore, induced EMF due to small element will be, d ε = B v d x = B ω x d x Integrating both sides, we get ∫ d ε = ∫ B ω x d x ⇒ ε = B ω ∫ 0 L x d x = B ω L 2 2