CBSE Class 12 Physics Chapter 1: Electric Charges and Fields NCERT Solutions

The problem states that $q_2$ and $q_3$ are positive charges, and they exert a net electric force on $q_1$ along the +x-direction. For a net force to be in the +x-direction, the individual forces exerted by $q_2$ and $q_3$ on $q_1$ must have components that add up along the +x-axis. Since $q_2$ and $q_3$ are positive, and they are located on the y-axis, the force they exert on $q_1$ (located on the x-axis) must be attractive if $q_1$ is negative, or repulsive if $q_1$ is positive. Given the net force is towards the +x direction, this implies that $q_1$ must be a negative charge, as the attractive forces from $q_2$ and $q_3$ would pull $q_1$ towards the region between them and along the x-axis.

Let's assume $q_1$ is at the origin $(0,0)$ for simplicity in analyzing directions, and $q_2$ and $q_3$ are at $(0, y_2)$ and $(0, y_3)$ respectively. The force exerted by $q_2$ on $q_1$ and $q_3$ on $q_1$ have resultant along +x-axis. This means $q_1$ is attracted towards the y-axis, implying $q_1$ is negative.

Now, a positive charge Q is introduced at $(x, 0)$ on the x-axis. Since Q is positive and $q_1$ is negative, there will be an attractive force between Q and $q_1$. This attractive force will be directed from $q_1$ towards Q, which is along the +x-direction.

Therefore, the introduction of positive charge Q adds another force component along the +x-direction to the existing net force on $q_1$. This means the total force on $q_1$ will increase in magnitude and will continue to point along the positive x-axis.

The correct option is (a).

When a point positive charge is brought near an isolated conducting sphere without touching it, the phenomenon of electrostatic induction occurs. The free electrons within the conducting sphere are attracted towards the positive point charge. These electrons accumulate on the surface of the sphere that is closer to the positive charge, creating a region of negative charge density.

As electrons move towards the near surface, the opposite side of the sphere is left with a deficiency of electrons, resulting in a net positive charge density on the surface farther from the point charge.

Electric field lines originate from positive charges and terminate on negative charges. In this scenario, electric field lines will originate from the external point positive charge and terminate on the induced negative charges on the near surface of the conducting sphere. Additionally, electric field lines will originate from the induced positive charges on the far surface of the sphere and extend outwards, eventually terminating at infinity or on other negative charges if present.

Furthermore, electric field lines are always perpendicular to the surface of a conductor in electrostatic equilibrium. Therefore, the field lines originating from the external positive charge must be perpendicular to the conducting surface where they terminate, and the field lines originating from the induced positive charge on the far side must also be perpendicular to that surface.

Figure (a) correctly depicts these conditions: electric field lines originate from the external positive charge, curve towards the conducting sphere, and terminate perpendicularly on the induced negative charge on the near surface. Field lines also originate perpendicularly from the induced positive charge on the far surface and extend outwards.

The correct option is (a).