Potential at a Point due to an Isolated Charge

The potential at a point in an electric field is a measure of the work done in bringing a unit positive charge from infinity to that point. In the case of an isolated charge, the potential at a point can be determined using the equation:

V = k(Q / r)

Where:
- V is the potential at the point
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- Q is the charge of the isolated charge
- r is the distance from the point to the isolated charge

In this case, we need to find the potential at a point located 0.1m away from an isolated charge of 100V. Let's calculate the potential using the given values:

V = (9 x 10^9 Nm^2/C^2) * (100C / 0.1m)

Simplifying the equation, we get:

V = 9 x 10^9 Nm^2/C * 1000C/m

V = 9 x 10^12 Nm/C

Thus, the potential at the point 0.1m away from the isolated charge is 9 x 10^12 volts.

Nature and Magnitude of the Point Charge

The potential at a point due to an isolated charge is directly proportional to the magnitude of the charge and inversely proportional to the distance from the charge. From the given information, we can determine the nature and magnitude of the point charge.

Nature:
Since the potential is positive, the charge must be positive. The point charge is therefore positive.

Magnitude:
To find the magnitude of the point charge, we rearrange the potential equation to solve for the charge:

Q = V * r / k

Substituting the values into the equation, we get:

Q = (9 x 10^12 Nm/C) * (0.1m) / (9 x 10^9 Nm^2/C^2)

Simplifying the equation, we have:

Q = 1 C

Thus, the magnitude of the point charge is 1 Coulomb.

Therefore, the nature of the point charge is positive and the magnitude is 1 Coulomb.