Question

three isolated equal charges are placed at three corners of an equilateral triangle as shown in the figure. The statement which is true for net electric potential V and net electric field intensity E at the centre of the circle is
a) E=0 , V=0
b) V=0 , E not equal to 0
c) V not equal to 0, E=0
d) V not equal to 0, E not equal to 0
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Answer 1

Answer:c

Explanation:V is scalar,so simple addition will not give 0

E is vector and vector addition gives 0

Answer 2

Answer:

The net electric field at the center is zero(E=0) but the net electric potential is not zero(V≠0).

(c) is correct.

Explanation:

Given that,

Three isolated equal charges are placed at three corners of an equilateral triangle.

The distance from any corner to center will be same and the electric field for any corner charge will be equal.

So the electric field due to +Q charges of edge 1 at center is

$E_{A}=\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{Q}{r^2}$

The electric field same as due to charges of edge 2 and 3.

$E_{1}=E_{2}=E_{3}$

The resultant of E₂ and E₃ is

$E_{r}=\sqrt{E_{2}^2+E_{3}^2+2E_{2}E_{3}\cos\theta}$

$E_{r}=\sqrt{E_{2}^2+E_{2}^2+2E_{2}E_{2}\cos120^{\circ}}$

Here, $E_{2}=E_{3}$

So, $E_{r}=\sqrt{E_{2}^2+E_{2}^2+2\times E_{2}^2\times\dfrac{-1}{2}}$

$E_{r}=\sqrt{E_{2}^2}$

$E_{r}=E_{2}$

E₁ and E₂ are equal in magnitude and in opposite direction.

The resultant electric field of any two charges will neutralize the electric field for the another.

So, The net electric field at the center will be zero.

For the electric potential is

Let us consider that the distance from the center to any charge is x.

The distance from any corner to center will be same.

So, the electric potential is

$V = \dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{q}{x}}$

The net electric potential

$V=3\times\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{q}{x}}$

So, The net electric potential is not equal to zero.

Hence, The net electric field at the center is zero(E=0) but the net electric potential is not zero(V≠0).