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 \[x,\text{ }y\]and \[z\]and plot the charges with the given coordinates as shown. O is the origin at which \[-2\text{ }q\]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 \[P=(a,a,0).\]The magnitude of resultant dipole moment is \[p'=\sqrt{{{p}^{2}}+{{p}^{2}}}=\sqrt{{{(qa)}^{2}}+{{(qa)}^{2}}}\] \[=\sqrt{2}\,qa\]You need to login to perform this action.
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