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JIPMER 2014
Exam
JIPMER
Year
2014
Subject
Physics
Chapter
Electrostatics

JIPMER 2014 · Physics · Electrostatics

Three points charges +q,-2 q and +q are placed at points (x=0, y=a,...

Three points charges +q,−2q+q,-2 q and +q+q are placed at points (x=0,y=a,z=0),(x=0,y=0,z=0)(x=0, y=a, z=0),(x=0, y=0, z=0) and (x=a,y=0,z=0)\quad(x=a, y=0, z=0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly areThree points charges +q,-2 q and +q are placed at points (x=0, y=a, z=0),(x=0, y=0, z=0) and (x=a, y=0, z=0) ,

Options

  1. A2qa\sqrt{2} q a along +y+y direction
  2. B2qa\sqrt{2} q a along the line joining points (x=0,y=0,z=0) and (x=a,y=a,z=0)(x=0, y=0, z=0) \text{ and }(x=a, y=a, z=0)
  3. Cqa along the line joining points (x=0,y=0,z=0)(x=0, y=0, z=0) and (x=a,y=a,z=0)(x=a, y=a, z=0)
  4. D2qa\sqrt{2} q a along +x+x direction

Correct answer

B. 2qa\sqrt{2} q a along the line joining points (x=0,y=0,z=0) and (x=a,y=a,z=0)(x=0, y=0, z=0) \text{ and }(x=a, y=a, z=0)

Step-by-step solution

OO is the origin at which −2q-2 q charge is placed. The system is equivalent to two dipoles along xx and yy-directions respectively. The dipole moments of two dipoles are shown in figure. Three points charges +q,-2 q and +q are placed at points (x=0, y=a, z=0),(x=0, y=0, z=0) and (x=a, y=0, z=0) , The resultant dipole moment will be directed along OPO P where P=(a,a,0)P=(a, a, 0). The magnitude of resultant dipole moment is p′=p2+p2=(qa)2+(qa)2=2qap^{\prime}=\sqrt{p^2+p^2}=\sqrt{(q a)^2+(q a)^2}=\sqrt{2} q a
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