Dimensional formula for Potential Gradient

The potential gradient is the rate of change of electric potential with distance. It is also known as the electric field or the electric field strength. The dimensional formula for potential gradient can be derived by using the formula for the electric field as follows:

Formula for Electric Field

The electric field is defined as the force per unit charge acting on a test charge. Hence, the formula for electric field is given as:

E = F/Q

Where,
E = Electric field strength
F = Force
Q = Charge

The unit of electric field is Newtons per Coulomb (N/C).

Formula for Potential Gradient

The potential gradient is the rate of change of electric potential with distance. Hence, the formula for potential gradient is given as:

V/d

Where,
V = Electric potential
d = Distance

The unit of potential gradient is Volts per meter (V/m).

Derivation of Dimensional Formula for Potential Gradient

The dimensional formula for potential gradient can be derived by substituting the dimensional formula for electric potential and distance in the formula for potential gradient as follows:

[V/d] = [ML2T-3A-1]/[L]

Simplifying the above equation, we get:

[V/d] = [M L T-3 A-1]

Hence, the dimensional formula for potential gradient is [M L T-3 A-1].

Conclusion

The dimensional formula for potential gradient is derived by substituting the dimensional formula for electric potential and distance in the formula for potential gradient. The unit of potential gradient is Volts per meter (V/m).