Let V and E be the potential and the field respectively at a point. Which of the following assertions are correct?

Question

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Answer 1

The electric field is $E = - \frac{d V}{d x}$
if $V = 0$ , we can not say E must be zero, we say only E may be zero.
if $V \neq = 0$ , E must be zero when V is max i.e, $\frac{d V}{d x} = 0$
if $E \neq = 0$ , V may be zero when two equal and opposite charges separated by a distance and at the midpoint in between the charges field non-zero but potential is zero.

Answer 2

The electric field is

E = - \frac{d V}{d x}

if

V = 0

, we can not say E must be zero, we say only E may be zero.
if

V \neq = 0

, E must be zero when V is max i.e,

\frac{d V}{d x} = 0

if

E \neq = 0

, V may be zero when two equal and opposite charges separated by a distance and at the midpoint in between the charges field non-zero but potential is zero.

Let V and E be the potential and the field respectively at a point. Which of the following assertions are correct?

If V $=$ 0, E must be zero.

If V $\neq =$ 0, E cannot be zero.

If E $\neq =$ 0, V cannot be zero.

none of these.

Mark the correct statement:

The electric field and the electric potential at a point inside a shell are E and V respectively. Which of the following is correct?

The electric field strength if the potential of field depends upon x, y coordinates as $V = a (x^{2} - y^{2})$ is:

The electric field and the electric potential at a point are E and V respectively. Then, the incorrect statements are :

A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be a point on the x-axis at x $= + 1 c m$ and C be the point on the y-axis at y $= + 1 c m$ . Then, the potential at points A, B and C satisfy :

Let V and E be the potential and the field respectively at a point. Which of the following assertions are correct?

If V = 0, E must be zero.

If V = 0, E cannot be zero.

If E = 0, V cannot be zero.

none of these.

Mark the correct statement:

The electric field and the electric potential at a point inside a shell are E and V respectively. Which of the following is correct?

The electric field strength if the potential of field depends upon x, y coordinates as V=a(x2−y2) is:

The electric field and the electric potential at a point are E and V respectively. Then, the incorrect statements are :

A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be a point on the x-axis at x =+1cm and C be the point on the y-axis at y =+1cm. Then, the potential at points A, B and C satisfy :

If V $=$ 0, E must be zero.

If V $\neq =$ 0, E cannot be zero.

If E $\neq =$ 0, V cannot be zero.

The electric field strength if the potential of field depends upon x, y coordinates as $V = a (x^{2} - y^{2})$ is:

A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be a point on the x-axis at x $= + 1 c m$ and C be the point on the y-axis at y $= + 1 c m$ . Then, the potential at points A, B and C satisfy :