# The relation between Electric Field and Electric Potential

• ItsAnshumaan
In summary: Again, I am a little hamstrung by the forum rules. Yes, there are pairs that are not logically equivalent, such as (a) and (c). Logically, (a) implies (c), but (c) does not imply (a).
ItsAnshumaan

## Homework Statement

The electric field and the electric potential at a point are E and V respectively.
(a) If E=0, V must be 0
(b) If V=0, E must be 0
(c) If E≠0, V cannot be 0
(d) If V≠0, E cannot be 0

[/B]
E = V/d

## The Attempt at a Solution

[/B]
I basically substituted the value of E and V as 0 in respective cases, but ended up getting (a) and (b) as true. I know this is a very fundamental question, but I just can't figure it out.

In your question, V is the absolute potential at the given point while electric field E=potential difference/d.

ItsAnshumaan said:

## Homework Statement

The electric field and the electric potential at a point are E and V respectively.
(a) If E=0, V must be 0
(b) If V=0, E must be 0
(c) If E≠0, V cannot be 0
(d) If V≠0, E cannot be 0

[/B]
E = V/d

## The Attempt at a Solution

[/B]
I basically substituted the value of E and V as 0 in respective cases, but ended up getting (a) and (b) as true. I know this is a very fundamental question, but I just can't figure it out.
Does anyone of them have to be true?

It looks like there are pairs of them which are logically equivalent.

Te electric field E and electric potential V are two separate functions. Although the potential depends on the electric field, they are not proportional and the potential depends on the integral of the electric field over a path. The forum rules don't allow simply giving the answer, but the answer is quite simple. @SammyS The pairs are not logically equivalent. The equation the OP presents that E=V/d does have precise proportionality between E and V, but this equation is very misleading because it does not apply in general. It is for the special case of an ideal capacitor and E is the uniform electric field between the plates and V is the voltage drop across the plates. The equation really does not apply here, and the capacitor equation does not give V at any location between the plates where the E field is present. Although it looks like the right equation, it is totally irrelevant to this problem.

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Te electric field E and electric potential V are two separate functions. Although the potential depends on the electric field, they are not proportional and the potential depends on the integral of the electric field over a path. The forum rules don't allow simply giving the answer, but the answer is quite simple. @SammyS The pairs are not logically equivalent.
Are you saying that there is no pair that are not logically equivalent?

From a pure logic point of view.

(P implies Q) is logically equivalent to ((not Q) implies (not P)) .

It appears to me that we can find cases where one of these statements is the contrapositive of another.

SammyS said:
Are you saying that there is no pair that are not logically equivalent?

From a pure logic point of view.

(P implies Q) is logically equivalent to ((not Q) implies (not P)) .

It appears to me that we can find cases where one of these statements is the contrapositive of another.
@SammyS It is somewhat difficult to answer your question without giving out the complete answer (at least what I am pretty certain is the correct answer), but none of the statements contains logical equivalence. To just give a counterexample for statement "d", a charged hollow conducting sphere has E=0 throughout the entire interior, but V is not equal to zero... editing.. And to give the OP something that might help them answer "b" and "c", what is the V and E for the point midway between two electrical charges of +Q and -Q? And I think the example I gave for "d" can also be used to answer "a".

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## What is the difference between electric field and electric potential?

Electric field refers to the force exerted by an electric charge on another charge. It is a vector quantity that describes the strength and direction of the force. On the other hand, electric potential is a scalar quantity that describes the potential energy per unit charge at a certain point in space.

## How are electric field and electric potential related?

The relationship between electric field and electric potential is given by the equation E = -∇V, where E is the electric field, V is the electric potential, and ∇ is the gradient operator. This means that the electric field is the negative gradient of the electric potential.

## What is the significance of electric potential in electrical systems?

Electric potential plays a crucial role in understanding and analyzing electrical systems. It helps in determining the direction of electric current flow, calculating the work done on a charge by an electric field, and predicting the behavior of charged particles in an electric field.

## How do changes in electric potential affect the electric field?

Changes in electric potential directly affect the electric field. An increase in electric potential results in a stronger electric field, while a decrease in electric potential results in a weaker electric field. This is because the electric field is directly proportional to the electric potential.

## What is the unit of electric potential and electric field?

The unit of electric potential is volts (V) while the unit of electric field is volts per meter (V/m). This can also be expressed as newtons per coulomb (N/C) since electric field is a measure of force per unit charge.

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