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 :
[b] 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 |
\[p'=\sqrt{{{p}^{2}}+{{p}^{2}}}\] |
\[=\sqrt{{{(qa)}^{2}}+{{(qa)}^{2}}}\] |
\[=\sqrt{2}\,qa\] |
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