# When is electric field zero and electric potential non zero

• mrcotton
In summary, the statement that is incorrect is that electric potential is zero whenever the electric field strength is zero.
mrcotton

## Homework Statement

Which one of the following statements about electric field strength and electric potential is
incorrect?
A Electric potential is a scalar quantity.
B Electric field strength is a vector quantity.
C Electric potential is zero whenever the electric field strength is zero.
D The potential gradient is proportional to the electric field strength.

E=K Q/(R^2)
V=K Q/R

K=1/(4∏ε)

## The Attempt at a Solution

If for example you had two positive charges of 3 coulombs a distance 4m apart.
The electrostatic field at the midpoint would be zero. Effectively a positive charge at this point would be push by an equal force in both directions.

However the Electric potential V would be 2*(k*(3/4)

So you can have a zero E with a non zero V

Is this logic ok
Thanks for any help

mrcotton said:

However the Electric potential V would be 2*(k*(3/4)

So you can have a zero E with a non zero V

Is this logic ok
Thanks for any help

The electrical potential goes as 1/r, but your reasoning is correct. You could also consider the electric potential and electric fields associated with spherical conductors: Provided the conductor is closed, the E field inside is 0 but the potential is a constant.

## 1. When is electric field zero and electric potential non zero?

The electric field is zero when there are no charges present in the given region. However, the electric potential can still be non-zero in this case if there are charges present in other regions that influence the potential at the given point.

## 2. Can electric field be zero and electric potential be non-zero at the same point?

Yes, this can happen if there are charges present in other regions that influence the potential at the given point, but there are no charges present at the given point itself.

## 3. What is the relationship between electric field and electric potential?

The electric field and electric potential are related through the equation E = -∇V, where E is the electric field, V is the electric potential, and ∇ represents the gradient operator. This means that the electric field is the negative gradient of the electric potential.

## 4. Why is electric field zero inside a conductor?

In a conductor, the charges are free to move and redistribute themselves in response to an external electric field. This redistribution causes the electric field inside the conductor to be canceled out, resulting in a zero electric field.

## 5. Can electric potential be negative?

Yes, electric potential can be negative. It is a scalar quantity and its sign depends on the direction of the electric field. A negative electric potential indicates that the electric field is directed towards the point where the potential is being measured.

• Introductory Physics Homework Help
Replies
10
Views
319
• Introductory Physics Homework Help
Replies
22
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
514
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
453
• Introductory Physics Homework Help
Replies
6
Views
582
• Introductory Physics Homework Help
Replies
2
Views
691
• Introductory Physics Homework Help
Replies
1
Views
363