Question

Which statement is true:
(a) A ring of radius R carries a uniformly distributed charge +Q. A point charge –q is placed on the axis of the ring at a distance 2R from the center of the ring and released from rest. The particle executes a simple harmonic motion along the axis of the ring.
(b) Electrons move from a region of higher potential to lower potential.
(i) only a
(ii) only b
(iii) a and b
(iv) none of them.

Answer 1

Here we have given two statements in which either one is right or both may be right (or wrong). For the first statement, we can draw the diagram and consider the forces and the motion of the charges to verify whether the statement is true or not. Whereas for the second statement we can discuss briefly the direction of the flow of electrons to verify the statement.

Complete step-by-step solution:
Let us consider the first statement which says that a point charge –q will have simple harmonic motion along the axis of the ring of radius R and uniformly distributed charge +Q when released from rest. The distance of point charge from the center of the ring is 2R. The diagrammatic representation of the given situation is given below

We can see that the ring has uniformly positive charges whereas the point charge is negative. As there will be an attractive force between the positive and negative charges, therefore, the point charge will have oscillatory motion or we can say simple harmonic motion due to the attractive force between the point charge and positive charge around the ring.
Hence the first statement is true.
Now the second statement says that electrons move from higher potential to lower potential but we know that electron is a negative charge therefore the electrons in an electric field moves from lower potential to a higher potential. So the second statement is false.
Hence option A is correct.

Note: In the first case when the particle moves in +x direction there will be an equal pull from x-direction and vice-versa resulting in oscillatory motion. We can also conclude directly that the second statement is false as the electron has a negative charge so it will move from negative to positive or towards positive. Hence the motion of electrons is from lower potential to higher potential.