Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
Determine the dimensions of the expression d _B dt . The symbols carry their usual meanings.
Options
- AML^2 I⁻² T⁻³
- BML^2 I⁻¹ T⁻³
- CML I⁻¹ T⁻²
- DML^2 I⁻¹ T⁻²
Correct answer
B. ML^2 I⁻¹ T⁻³
Step-by-step solution
According to Faraday's law of electromagnetic induction, the induced electromotive force (EMF) is given by e = - d _B dt . Thus, the dimensions of d _B dt are the same as the dimensions of electric potential or EMF. Electric potential is defined as work done per unit charge, V = W q . The dimensional formula for work is [W] = ML^2 T⁻² . The dimensional formula for charge is [q] = IT . Therefore, the dimensions of d _B dt are ML^2 T⁻² IT = ML^2 I⁻¹ T⁻³ .