Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential
The electric potential in a region of space is given by V(x, y, z) = A(xy + yz + zx) . Determine the dimensional formula of A .
Options
- A[M L^2 T⁻³ I⁻¹]
- B[M T⁻² I⁻¹]
- C[M T⁻³ I⁻¹]
- D[M L T⁻³ I⁻¹]
Correct answer
C. [M T⁻³ I⁻¹]
Step-by-step solution
Electric potential is defined as work done per unit charge, V = W q . The dimensional formula of work W is [M L^2 T⁻²] and that of charge q is [I T] . The dimensional formula of electric potential V is [M L^2 T⁻²] [I T] = [M L^2 T⁻³ I⁻¹] . Given the relation V(x, y, z) = A(xy + yz + zx) , the term (xy + yz + zx) represents the product of two lengths, so its dimensional formula is [L^2] . Using the principle of dimensional homogeneity, the dimensional formula of A is: [A] = [V] [L^2] = [M L^2 T⁻³ I⁻¹] [L^2] = [M T⁻³