Question

Calculate the dimensions of (a) ∫→E.d→l, (b) vBl and (c) dΦBdt. The symbols have their usual meaning.

Answer 1

Make Calculations on Basis of Formula

Explanation:

Since, the Quantity $\int \underset{E}{\rightarrow}.\underset{d}{\rightarrow}$, can also be written as -

$\int \underset{E}{\rightarrow}.\underset{d}{\rightarrow}$, = V .... (V = Voltage)

Unit of voltage is

Voltage can be written as -

Voltage = $\frac {Energy}{Charge}$

Dimensions of Energy = $ML^2T^-^2$

Dimensions of Charge = [IT]  

The Dimensions made after calculations, on the basis of above data, have been represented as -  

(a) $\int E.dl = MLT^-^3 I^-^1 \times L = ML^2I^-^1T^-^3$

(b) $\varphi BI = LT^-^1 \times MI^-^1T^-^2\times L = ML^2I^-^1T^-^3$  

(c) $\frac {d\phi_s}{dt} = ML^-^1T^-^2 \times L^2 = ML^2I^-^1T^-^2$