1

Question

Two charges 5 ×
10^{−8} C and −3 × 10^{−8} C
are located 16 cm apart. At what point(s) on the line joining the two
charges is the electric potential zero? Take the potential at
infinity to be zero.

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Solution

There are two charges,

Distance between the
two charges, *d* = 16 cm = 0.16 m

Consider a point P on the line joining the two charges, as shown in the given figure.

*r* = Distance of
point P from charge *q*_{1}

Let the electric
potential (*V*) at point P be zero.

Potential at point P is
the sum of potentials caused by charges *q*_{1} and *q*_{2}
respectively.

Where,

= Permittivity of free space

For *V* = 0,
equation (i) reduces to

Therefore, the potential is zero at a distance of 10 cm from the positive charge between the charges.

Suppose point P is
outside the system of two charges at a distance *s *from the
negative charge, where potential is zero, as shown in the following
figure.

For this arrangement, potential is given by,

For *V* = 0,
equation (ii) reduces to

Therefore, the potential is zero at a distance of 40 cm from the positive charge outside the system of charges.

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