Home
Class 12
PHYSICS
Conisder a system of three charges q//3,...

Conisder a system of three charges `q//3`, `q//3` and `-2q//3` placed at point A, B and C, respectively, as shown in the figure. Take O to be centre of the circle of radius R and angle `CAB=60^@`

A

(a) The electric field at point O is `(q)/(8pi epsilon_0R^2)` directed along the negative x-axis.

B

(b) The potential energy of the system is zero

C

(c) The magnitude of the force between the charges at C and B is `(q^2)/(54pi epsilon_0R^2)`

D

(d) the potential at point O is `(q)/(12pi epsilon_0R)`

Text Solution

Verified by Experts

The correct Answer is:
C
The electric field due to A and B at O are equal and oppoiste producing a resultant which is zero. The electric field at O due to C is
`E=(1)/(4piin_0)(2q//3)/(R^2)=(q)/(6piin_0R^2)`.
`:.` Option [A] is not correct. The electric potential at O is

`V_O=K[(+q//3)/(R)]+K[(+q//3)/(R)]+K[(-2q//3)/(R)]=0`
`:.` Option [D] is wrong
In `DeltaABC(AC)/(AB)=isn 30^@impliesAC=(AB)/(2)=R`
Also `(BC)/(AB)=isn 60^@impliesBC=(sqrt(3)AB)/(2)=sqrt(3)R`
Potential energy of the system
`K[((q//3)(2//3))/(2R)]+K[((q//3)(-2q//3))/(R)]+K[((q//3)(-2q//3))/(sqrt3R)]`
`=(kq^2)/(9R)[1/2-2-2/sqrt3]!=0`
`:.` Option [B] is wrong
Magnitude of force between B and C is
`F=(1)/(4piin_0)((2q//3)(q//3))/(sqrt3R)^2=(q^2)/(54piin_0R^2)`
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

Consider a system of three charges (q)/(3),(q)/(3) and -(2q)/(3) placed ar point A,B and C respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60^(@) . Choose the incorrect options (1) The electric field at point O is (q)/(8 pi epsilon_(0)R^(2)) directed along the negative x-axis (2) The potential energy of the system is zero (3) The potential at point O is (q)/(12 pi epsilon_(0) R) (4) The magnitude of the force between the charges at C and B is (q^(2))/(54 pi epsilon_(0) R^(2))

Figure shows three charges -q,+q, and -2q kept at points A,B and C respectivley. OA =OB=OC=r. The electric field inteinsity at O has a magnitude of

Charges q, 2q,3q and 4q are placed at the corners A,B,C and D of a square as shown in the following figure. The directon of electric field at the centre of the square is along

Charges 1q, 2q, 3q and 4q are placed at the corners A,B,C and D of a square as shown in Fig. The direction of electric field at the centre of square is along :

Three charges -q_1 , +q_2 and -q_3 are placed as shown in the figure. The x-component of the force on -q_1 is proportional to

The value of charge q_1 ,q_2 and q_3 as shown in the figure are

Four point charges Q.q Q and q are placed at the corners of a square side 'a' as shown in the figures. Find the Potential energy of this system.

Three charges -q_(1), +q_(2) and -q_(3) are placed as shown in the figure. The x -component of the force on -q_(1) is proportional to

Three charges of (+2q), (-q) and (-q) are placed at the corners A,B and C of an equilateral triangle of side a as shown in the adjoining figure. Then the dipole moment of this combination is