Question

A metallic sphere is placed in a uniform electric field. Which one of the paths a, b, c, and d showed in the figure will be followed by the field lines and why?

Answer 1

Hint: Try to figure out the characteristic features of the electric field lines inside a conductor as the sphere is metallic and metals are good conductors. We will also have to find out how the free charges inside a conductor will react in the presence of an external electric field. Also, we have to keep in mind that the field lines are always drawn normally to the surface. All these evaluations will help to reach the answer.

Complete Step By Step answer:
The concept of the electric field lines was first discovered by Michael Faraday in the 1830s. The electric lines of forces are the imaginary path on which a unit positive test charge moves or it is an imaginary curve, to which if a tangent is drawn at a point gives the direction of the intensity of the electric field at that point. The electric field lines usually originate from the positive charge and terminate at the negative charge.
Now, the question shows different paths followed by electric field lines inside a metallic sphere. As the sphere is metallic, it can be considered as a conductor.
A conductor contains a large number of free electrons which moves under the influence of the external electric field. So, when a conductor is placed in a uniform external electric field, the free charges inside the conductor starts to move under the influence of the external field and rearrange themselves in such a manner that the net internal field due to accumulation of charges has the exact same strength as the external field. Therefore the net field inside a conductor is zero and charges reside only on the surface of the conductor.

As there is no electric field inside the conductor, there will be no electric field lines inside it. We can infer from the diagram that the paths a, b, and c are passing through the inner surface of the conductor which contradicts the result that the electric field is zero inside the conductor. Therefore, paths a, b and c cannot be the electric field lines of the conductor.
Due to the external field, the charge gets accumulated on the surface of the conductor as shown in the figure and there is no electric field inside the conductor and hence no field lines.

We know that electric field lines originate from a positive charge and terminate at a negative charge. As negative charge is accumulated on the left side, the field lines are terminating and the positive charge gets accumulated on the right side therefore the field lines are originating from it.
Hence, the electric field line will follow the path.

Note:
The electric lines of forces never intersect each other because if they do so, then at the point of intersection the net intensity will have two different directions which is not possible. As the work done by the electric field is conservative in nature, the electric field lines cannot form a closed loop as the work done around a closed in will not be zero which contradicts the conservative nature of the field.