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

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, $\frac{d V}{d x} = 0$ For example, inside the conductor $E = 0,$ but $V \neq = 0$
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 is 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

For example, inside the conductor

E = 0,

but

V \neq = 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 is non-zero but potential is zero.

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

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

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

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

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

Figure shows three points A, B and C in a region of uniform electric field $E$ . The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good. Here $V_{A}, V_{B}$ and $V_{C}$ represents the electric potential at point A, B and C respectively.

In a certain region the electric potential at a point $(x, y, z)$ is given by the potential function $V = 2 x + 3 y - z$ . Then the electric field in this region will :

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

A, B and C are three points in a uniform electric field. The electric potential is :

The electric potential V at any point (x, y, z), all in meters in space is given by $V = 4 x^{2}$ volt. The electric field at the point (1, 0, 2) in volt/meter is :

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

If E = 0, V must be zero.

If V = 0, E must be zero.

If E = 0, V cannot be zero.

If V = 0, E cannot be zero.

Figure shows three points A, B and C in a region of uniform electric field E. The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good. Here VA​,VB​ and VC​ represents the electric potential at point A, B and C respectively.

In a certain region the electric potential at a point (x,y,z) is given by the potential function V=2x+3y−z. Then the electric field in this region will :

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

A, B and C are three points in a uniform electric field. The electric potential is :

The electric potential V at any point (x, y, z), all in meters in space is given by V=4x2 volt. The electric field at the point (1, 0, 2) in volt/meter is :

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

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

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

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

Figure shows three points A, B and C in a region of uniform electric field $E$ . The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good. Here $V_{A}, V_{B}$ and $V_{C}$ represents the electric potential at point A, B and C respectively.

In a certain region the electric potential at a point $(x, y, z)$ is given by the potential function $V = 2 x + 3 y - z$ . Then the electric field in this region will :

The electric potential V at any point (x, y, z), all in meters in space is given by $V = 4 x^{2}$ volt. The electric field at the point (1, 0, 2) in volt/meter is :