# We have seen that an electric field must exist inside a conductor that carries a current. How is that possible in view of the fact that in electrostatics we concluded that the electric field must be zero inside a conductor?

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

#### Solutions

Chapter
Section
Chapter 17, Problem 1CQ
Textbook Problem

## We have seen that an electric field must exist inside a conductor that carries a current. How is that possible in view of the fact that in electrostatics we concluded that the electric field must be zero inside a conductor?

Expert Solution
To determine
The reason for existence of electric field in a current carrying conductor given that the electric field is zero inside conductor in case of electrostatics.

Electric potential gradient creates the electric field inside current carrying conductor. Since no potential gradient, no electric field inside conductor in electrostatic condition.

### Explanation of Solution

Existence of electric field in a current carrying conductor can be explained by the concept of electric potential gradient. Electric potential gradient is the change in electric potential with distance moved by charge.

In electrostatics, charges are stationary because the electric potential is same at every point of conductor means no potential gradient. So from the relation E=ΔV , where E is the electric field and ΔV is the potential gradient. E=0 inside conductor in electrostatic condition. For a current carrying conductor, charges can move because the potential is continuously decreasing. Since there is a potential gradient in current carrying conductor, from E=ΔV electric field is non-zero inside the current carrying conductor.

Conclusion: Electric potential gradient creates the electric field inside current carrying conductor. Since no potential gradient, no electric field inside conductor in electrostatic condition.

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