Electrostatics

Step 1: Recall the work-energy theorem

The work done on an object is equal to the change in its kinetic energy. In this case, the work done on the object by the electric field is converted into its kinetic energy. The work done by the electric field is given by:

where:
- is the charge of the object,
- is the electric field strength,
- is the displacement of the object in the direction of the electric field.

The kinetic energy gained by the object is given by:

where is the mass of the object, and is its velocity at a distance m.

Step 2: Use the work-energy theorem

We are told that the object starts from rest, so its initial kinetic energy is zero. The kinetic energy at m is 0.12 J. Therefore, the work done on the object is equal to this change in kinetic energy:

Thus, the work done by the electric field is:

Substitute the known values:
- ,
- ,
- .

We can now solve for :

Final Answer: The charge is , which matches option (C).

Given:

• A uniform electric field exists along the horizontal direction.
• The electric potential at point A is .
• A small charge is moved slowly from point A to point B along a curved path.

Step 1: Expression for Potential Energy

The potential energy of the charge at point B is given by:

Answer: The correct option is D.

Given:

• A positively charged glass rod is brought near an uncharged metal sphere.
• The sphere is mounted on an insulated stand.
• The glass rod is then removed.

Step 1: Understanding Electrostatic Induction

When a charged object (glass rod) is brought near a conductor (metal sphere), it induces charge separation. The negative charges in the metal sphere move towards the glass rod, while the positive charges move away.

Step 2: What Happens When the Glass Rod is Removed?

Since the metal sphere is not grounded and no charge transfer has occurred, the charge redistribution disappears after removing the glass rod. The net charge on the sphere remains zero.

Answer: The correct option is A (Zero).

The electric susceptibility is defined as: where is the polarization of the material, is the permittivity of free space, and is the external electric field. The polarization is the dipole moment per unit volume.
Since there are 100 molecules and each has a dipole moment of , the total dipole moment is:

Now, substituting the values into the formula: