# Physics Class 12 NCERT Solutions: Chapter 2 Electrostatic Potential and Capacitance Part 6

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Q: 14. Two tiny spheres carrying charges are located apart. Find the potential and electric field:

(A) At the mid-point of the line joining the two charges, and

(B) At a point 10 cm from this midpoint in a plane normal to the line and passing through the mid-point.

Answer:

Two charges placed at points A and B are represented in the given figure. O is the mid- point of the line joining the two charges.

Magnitude of charge located at

Magnitude of charge located at

Distance between the two charges,

(A) Let and are the electric potential and electric field respectively at.

Potential due to charge at Potential due to charge at

Where,

Permittivity of free space

Electric field due to Electric field due to

Therefore, the potential at mid-point is and the electric field at mid-point is . The field is directed from the larger charge to the smaller charge.

(B) Consider a point Z such that normal distance, as shown in the following figure.

and are the electric potential and electric field respectively at . It can be observed from the figure that distance,

Electric field due to,

Electric field due to

The resultant field intensity at,

Where, is the angle

From the figure, we obtain

Therefore, the potential at a point (perpendicular to the mid-point) is and electric field is.