Question
Two point charges $$ + q$$ and $$ - q$$ are held fixed at $$\left( { - d,o} \right)$$ and $$\left( {d,o} \right)$$ respectively of a $$x-y$$ coordinate system. Then
A.
The electric field $$E$$ at all points on the $$x$$-axis has the same direction
B.
Electric field at all points on $$y$$-axis is along $$x$$-axis
C.
Work has to be done in bringing a test charge from $$\infty $$ to the origin
D.
The dipole moment is $$2qd$$ along the $$x$$-axis
Answer :
Electric field at all points on $$y$$-axis is along $$x$$-axis
Solution :
The two charges form an electric dipole. If we take a point $$M$$ on the $$X$$-axis as shown in the figure, then the net electric field is in $$X$$-direction.
$$\therefore $$ Option (A) is incorrect. If we take a point $$N$$ on $$Y$$-axis, we find net electric field along $$+X$$ direction.The same will be true for any point on $$Y$$-axis. (B) is a correct option.
NOTE : For any point on the equatorial line of a dipole, the electric field is opposite to the direction of dipole moment.
(B) $${W_{\infty - 0}} = q\left( {{V_\infty } - {V_0}} \right) = q\left( {0 - 0} \right) = 0$$
$$\therefore $$ (C) is incorrect. The direction of dipole moment is from -ve to + ve. Therefore (D) is incorrect.
The two charges form an electric dipole. If we take a point $$M$$ on the $$X$$-axis as shown in the figure, then the net electric field is in $$X$$-direction.
$$\therefore $$ Option (A) is incorrect. If we take a point $$N$$ on $$Y$$-axis, we find net electric field along $$+X$$ direction.The same will be true for any point on $$Y$$-axis. (B) is a correct option.
NOTE : For any point on the equatorial line of a dipole, the electric field is opposite to the direction of dipole moment.
(B) $${W_{\infty - 0}} = q\left( {{V_\infty } - {V_0}} \right) = q\left( {0 - 0} \right) = 0$$
$$\therefore $$ (C) is incorrect. The direction of dipole moment is from -ve to + ve. Therefore (D) is incorrect.
