Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
Determine the dimensions of the expression E d l . The symbols carry their usual meanings.
Options
- AML^2 I⁻² T⁻²
- BML^2 I⁻¹ T⁻³
- CML^2 I⁻¹ T⁻²
- DML^3 I⁻¹ T⁻³
Correct answer
B. ML^2 I⁻¹ T⁻³
Step-by-step solution
The expression E d l represents the line integral of the electric field, which corresponds to electric potential or electromotive force. Electric field E is defined as force per unit charge, E = F q . The dimensions of force F are [M L T⁻²] and the dimensions of charge q are [I T] . Therefore, the dimensions of E are [M L T⁻²] [I T] = [M L I⁻¹ T⁻³] . The term d l represents an infinitesimal length, which has dimensions [L] . The dimensions of E d l are the product of the dimensions of E and d l . Dimensions = [M L