Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
Determine the dimensions of the expression vBl . The symbols carry their usual meanings.
Options
- AM L I⁻¹ T⁻²
- BML^2 I⁻¹ T⁻³
- CML^2 I⁻¹ T⁻¹
- DML^2 I⁻² T⁻³
Correct answer
B. ML^2 I⁻¹ T⁻³
Step-by-step solution
The expression vBl represents the motional electromotive force (emf). The dimensions of emf are the same as those of electric potential, which is work done per unit charge. Dimensions of work W = [M L^2 T⁻²] Dimensions of charge q = [I T] Dimensions of vBl = [M L^2 T⁻²] [I T] = [M L^2 T⁻³ I⁻¹] Alternatively, using individual dimensions: [v] = [L T⁻¹] [B] = [F] [q][v] = [M L T⁻²] [I T][L T⁻¹] = [M T⁻² I⁻¹] [l] = [L] [vBl] = [L T⁻¹] [M T⁻² I⁻¹] [L] = [M L^2 T⁻³ I⁻¹]