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
Here's the solution to the problems: b) (i) Step 1: Define power in terms of work and time. Power (P) is the rate at which work (W) is done. P = (W)/(t) Step 2: Express work in terms of force and distance, and force in terms of mass and acceleration. Work (W) = Force (F) × Distance (L) Force (F) = Mass (M) × Acceleration (a) Acceleration (a) = DistanceTime^2 = L T^-2 Step 3: Substitute the fundamental quantities (Mass M, Length L, Time T) into the equations. F = M × (L T^-2) = M L T^-2 W = (M L T^-2) × L = M L^2 T^-2 P = M L^2 T^-2T = M L^2 T^-3 The dimensional equation of power is M L^2 T^-3. b) (ii) Step 1: Determine the dimensions of each quantity in the LMTI system. Energy density (W_d) is energy per unit volume. Energy (E) has dimensions M L^2 T^-2. Volume (Vol) has dimensions L^3. [W_d] = ([E])/([Vol]) = M L^2 T^-2L^3 = M L^-1 T^-2 Distance (d) has dimensions L. [d] = L Voltage (V) is work per unit charge. Charge (Q) = Current (I) × Time (T). [V] = ([W])/([Q]) = M L^2 T^-2I T = M L^2 T^-3 I^-1 Permittivity () can be derived from Coulomb's law $F