CBSE Class 12 · 2005 · All India · ElectrostaticsShort Answer

Two fixed point charges

+ 4 e

and

+ e

units are separated by a distance

a

. Where should the third point charge be placed for it to be in equilibrium?

Answer: At a distance $\frac{2 a}{3}$ from the $+ 4 e$ charge (on the line joining the two charges).

Solution

Let the third charge be at distance

x

from

+ 4 e

, hence

(a - x)

from

+ e

. For it to be in equilibrium the two forces must balance:

\frac{k ( 4 e ) q}{x ^{2}} = \frac{k ( e ) q}{( a - x ) ^{2}}

. So

\frac{4}{x ^{2}} = \frac{1}{( a - x ) ^{2}}

, giving

2 (a - x) = x

, i.e.

x = \frac{2 a}{3}

. The charge is placed at

\frac{2 a}{3}

from

+ 4 e

CBSE Class 12 Board · 2005 · All India · Subjective

Practise more: all CBSE board PYQs on Electrostatics →

More board questions on Electrostatics

Assertion (A): Equal amounts of positive and negative charges are distributed uniformly on two halves of a thin circular ring as shown in the figure. The resultant electric field at the centre O of the ring is along OC. Reason (R): It is so because the net potential at O is not z …
CBSE 2024View solution →
Four point charges of $1 μ C$ , $- 2 μ C$ , $1 μ C$ and $- 2 μ C$ are placed at the corners A, B, C and D respectively of a square of side 30 cm. Find the net force acting on a charge of $4 μ C$ placed at the centre of the square.
CBSE 2024View solution →
Three point charges $1 pC$ each are kept at the vertices of an equilateral triangle of side 10 cm. Find the net electric field at the centroid of the triangle.
CBSE 2024View solution →
(a)(i) Draw equipotential surfaces for an electric dipole. (ii) Two point charges $q_{1}$ and $q_{2}$ are located at $r_{1}$ and $r_{2}$ respectively in an external electric field $E$ . Obtain an expression for the potential energy of the system. (iii) The dipole moment …
CBSE 2024View solution →
(b)(i) A thin spherical shell of radius $R$ has a uniform surface charge density $σ$ . Using Gauss's law, deduce an expression for the electric field (i) outside and (ii) inside the shell. (ii) Two long straight thin wires AB and CD have linear charge densities …
CBSE 2024View solution →
The magnitude of the electric field due to a point charge object at a distance of 4.0 m is 9 N/C. From the same charged object the electric field of magnitude 16 N/C will be at a distance of
CBSE 2023View solution →