Home
Class 12
PHYSICS
Three charges each of value q are placed...

Three charges each of value q are placed at the corners of an equilateral triangle. A fourth charge Q is placed at the center of the triangle.
a. Find the net force on charge q.
b. If `Q = -q`, will the charges at the corners move toward the center or fly away from it ?
c. For what value of Q and O will the charges remain stationary ?
d. In situation (c), how much work is done in removing the charges to infinity ?

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
(i) The force on charge q kept at A due to charges kept at B and C
`F_1=2Fcos30^@`
`F_1=sqrt3xx(9xx10^9(q^2)/(a^2))`
The force on q due to charge `(-q)` kept at D
`F_2=9xx10^9(q^2)/(2a//3)^2=9/4xx(9xx10^9xx(q^2)/(a^2))`
Clearly the two forces are not equal. Also as `F_2gtF_1` the charges will move towards the centre.


(ii) For charges to remain stationary
`2xxK(q^2)/(a^2)xxsqrt3/2=9/4xxKxx(q^2Q)/(a^2)implies(4sqrt3q)/(9)=Q`
The charge Q should be negative.
The potential energy of the system is
`=3[K(q^2)/(a^2)+K(q^2)/(a^2)]+3[Kxx(4sqrt3)/(9)(qxxq)/((2a//3)^2)]`
`=6Kxx(q^2)/(a^2)+3sqrt3K(q^2)/(a^2)=3(2+sqrt3)K(q^2)/(a^2)`
This is the amount of work needed to move the charges to infinity.
Promotional Banner

Topper's Solved these Questions

  • ELECTROSTATICS

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise Subjective Problems|2 Videos

  • ELECTROSTATICS

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise Comprehension Based Questions|2 Videos

  • ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise JEE Main And Advanced|107 Videos

  • MODERN PHYSICS

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise MCQ (One Correct Answer|1 Videos

Similar Questions

Explore conceptually related problems

Three charges each of value q are placed at the corners of an equilateral triangle. A fourth charge Q is placed at the centre of the triangle. If Q = -q :

Three charges, each of value q, are placed at the corners of an equilateral triangle. A fourth charge Q is placed at the centre O of the triangle. (a) If Q = -q , will the charges at corners starts to move towards centre of away from it. (b) For what value of Q at O will the charges remain stationary ?

Three equal charges, each +q are placed on the corners of an equilatreal triangel . The electric field intensity at the centroid of the triangle is

Three charges each of magnitude q are placed at the corners of an equilateral triangle, the electrostatic force on the charge place at the centre is (each side of triangle is L )

Three charges +q,+q and -q are located at the corners of an equilaterial triangle of side a. Calculate potential energy of the system.

Three charges +Q each are placed at the corners A,B and C of an equilateral triangle. At the circumcenre, O the electric field wil be

Three charges 2q, -q, and -q are located at the vertices of an equilateral triangle. At the center of the triangle,

Three charge -q,+q and -q are placed at the cornors of an equilateral triangle of side a The resultant electric froce an a charge +q placed at a the centroid O of the triangle is