Question

State the formula giving relation between electric field intensity and potential gradient.

Hint:

Electric field intensity is always directed from higher to lower potential. The steeper the potential gradient, the stronger the electric field.

Answer 1

Step 1: Understanding the relationship.
The electric field intensity \( E \) is the rate of change of electric potential \( V \) with respect to distance \( x \).
Step 2: Formula for electric field intensity.
The formula for the electric field intensity \( E \) in terms of potential gradient is: \[ E =
- \frac{dV}{dx} \] where \( dV \) is the change in potential and \( dx \) is the change in distance. The negative sign indicates that the electric field points in the direction of decreasing potential.
Step 3: Conclusion.
The electric field intensity is the negative of the rate of change of electric potential with respect to distance.