A) \[\sqrt{2}\,qa\] along \[+y\] direction
B) \[\sqrt{2}\,qa\] along the line joining points \[(x=0,y=0,z=0)\] and \[(x=a,y=a,z=0)\]
C) \[qa\] along the line joining points \[(x=0,y=0,z=0)\] and \[(x=a,y=a,z=0)\]
D) \[\sqrt{2}qa\] along \[+x\] direction
Correct Answer: B
Solution :
Key Idea Electric dipole moment is a vector Quantity directed from negative charge to the similar positive charge. Choose the three coordinate axes as x, y and z and plot the charges with the given coordinates as shown. O is the origin at which -2q charge is placed. The system is equivalent to two dipoles along x and y-directions respectively. The dipole moments of two dipoles are shown in figure. The resultant dipole moment will be directed along OP where \[P\equiv (a,a,0),\]The magnitude of resultant dipole moment is \[P'=\sqrt{{{P}^{2}}+{{P}^{2}}}=\sqrt{{{(qa)}^{2}}+{{(aq)}^{2}}}\] \[=\sqrt{2}qa\]You need to login to perform this action.
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