What is the electric field inside a metallic sphere with point charges nearby?

[Saitama]

Homework Statement

Homework Equations

The Attempt at a Solution

The point P is inside the sphere, the electric field should be zero but there is no such option. The answer is given as (a). I don't understand how (a) could be the electric field due to the metallic sphere. Will the point charges affect the charge of sphere? If so, then how and why?

 

[collinsmark]

Homework Statement

Homework Equations

The Attempt at a Solution

The point P is inside the sphere, the electric field should be zero

You are correct.

but there is no such option.

Wait, hold on. The total electric field at point P is zero. The problem statement only asks about the electric field due to the metallic sphere.

The answer is given as (a). I don't understand how (a) could be the electric field due to the metallic sphere. Will the point charges affect the charge of sphere? If so, then how and why?

Well, you know that the total electric field at point P is zero. And there are three contributors to the electric field, charge q₁, charge q₂, and the metallic sphere.

$$\vec E_{q_1} + \vec E_{q_2} +\vec E_{sphere} = 0.$$

Solve for the magnitude $\left| E_{sphere} \right|$

As for the question of "why",

1. The static electric field within a conductor (i.e. within the conducting material itself; inside the metal itself) is always zero.
2. If a charge is brought near a conducting object, it will induce a surface charge distribution on the surface of the conducting object to ensure that the electric field in the conducting material itself is zero. The surface charge distribution will automatically arrange itself in whatever way it takes to ensure that that the electric field in the conductor is zero.

In this case, the surface charge distribution on the outer surface aligns itself in such a way to force the electric field inside the metal to be zero, by counteracting charges q₁ and q₂.

 

[Saitama]

Thank you for your explanation collinsmark. I understand it now.