Question

A hollow conducting sphere has a net charge of $+Q$. There are four labelled points all on the inside of the sphere, as shown below. Points A through D are located progressively closer to the centre of the sphere. Which point has the largest magnitude of electric field?

A. Point A
B. Point B
C. Point C
D. Point D
E. All points have the same magnetic field.

Answer 1

To solve the above question given to us where we have to find out which of the above given points in the hollow sphere has the largest magnetic field, we will use the Gauss’s theorem as we have a hollow sphere with a net charge of $+Q$on the surface of the given hollow sphere.

Complete step-by-step solution:
In the above question a hollow sphere is given with a net charge of $+Q$with four labelled points A, B, C and D present inside the hollow sphere and we have to find which point has the largest magnitude of electric field.
To solve the above question, we will use Gauss’s theorem which says that:
Gauss theorem says that the total electric flux out of any closed surface is always equal to the charge that is enclosed divided by the permittivity. The electric flux in an area can be given as an electric field multiplied by the area of the surface projected in the plane and perpendicular to the field
The net flux through any closed surface here is a hollow sphere is directly proportional to the net charge in the volume enclosed by the closed surface.
If we find out the electric field inside the hollow sphere, we will come to the conclusion that the electric field is equal to zero. As we know that all the given points A, B, C, D are inside the hollow sphere that means they will have electric field as zero only because the net charge in the hollow sphere is same for all the points that is equal to $+Q$and the net flux or charge is directly proportional to the electric field inside any closed surface
Hence, we can say that all the given points inside the hollow sphere will have the same electric field.
That means option (E) is the correct answer.

Note: The electric field of any object is the basic concept to know about electricity. The electric field of the surface of the object is calculated by applying Coulomb's law, but to find the electric field distribution in any closed surface, we must understand the concept of Gauss law. It helps in explaining the electric charge enclosed in a closed surface or the electric charge present in the enclosed closed surface.