Dimensional formula for displacement current

Displacement current is defined as:

$$I_d = \varepsilon_0 \frac{d\phi_E}{dt}$$

Where:

• I_d is the displacement current (in amperes)
• ε_0 is the electric constant, also known as the permittivity of free space (in farads per meter)
• Φ_E is the electric flux (in volts per meter)
• dΦ_E/dt is the rate of change of the electric flux with respect to time (in volts per meter per second)

To find the dimensional formula of displacement current, we can substitute the dimensions of the electric constant, electric flux, and time derivatives of electric flux into the above equation:

$$[I_d] = [\varepsilon_0] \left[\frac{d\phi_E}{dt}\right]$$

= [F/m] [V/m/s]

= [C/V] [V/m/s]

= [C/(V.m/s)]

= [A]

Therefore, the dimensional formula of displacement current is [A] (amperes).