This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Potential difference from electrostatics Pd = (k q)/(r) where [k] = N · m^2 · C^-2, [q] = C, [r] = m. Substitute dimensions: [Pd] = [N · m^2 · C^-2] · [C][m] = N · m · C^-1. Step 2: Dimensions of force [N] = [F] = M L T^-2. Thus, [Pd] = (M L T^-2) · L · C^-1 = M L^2 T^-2 C^-1. Step 3: Dimensions of charge [C] = [A · s] = I T. Substitute: [Pd] = M L^2 T^-2 · (I T)^-1 = M L^2 T^-2 · I^-1 T^-1 = M L^2 T^-3 I^-1. Step 4: Confirm from work per unit charge Work done = F · r, so [work] = (M L T^-2) · L = M L^2 T^-2. [Pd] = [work][q] = M L^2 T^-2I T = M L^2 T^-3 I^-1. Step 5: E.M.F. has same dimensions as electric potential difference. [Pd] = M L^2 T^-3 I^-1