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Question

A and B are two points on the axis and the perpendicular bisector respectively of a electric dipole. A and B are far away from the dipole and at equal distance from it. The field at A and B are :

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Solution

The correct option is **C** →EA=−→2EB

The electric field intensity due to the dipole at the point A on the axis of the dipole is given by

EA=2kpr3......(1)

where, p is electric dipole moment, r is the distance of point A from dipole and k=14πϵ0

The direction of the electric field E is along the axis of the dipole from the negative charge towards the positive charge.

Also, The electric field intensity due to the dipole at the point B on the perpendicular bisector of the dipole is given by

EB=kpr3......(2)

The direction of the electric field E is parallel to the axis of the dipole from the positive charge towards the negative charge.

Hence, direction of electric field intensity due to the dipole at the point A is opposite to that of at point B.(refer the figure)

From (1) and (2), we get

→EA=−2→EB

The electric field intensity due to the dipole at the point A on the axis of the dipole is given by

EA=2kpr3......(1)

where, p is electric dipole moment, r is the distance of point A from dipole and k=14πϵ0

The direction of the electric field E is along the axis of the dipole from the negative charge towards the positive charge.

Also, The electric field intensity due to the dipole at the point B on the perpendicular bisector of the dipole is given by

EB=kpr3......(2)

The direction of the electric field E is parallel to the axis of the dipole from the positive charge towards the negative charge.

Hence, direction of electric field intensity due to the dipole at the point A is opposite to that of at point B.(refer the figure)

From (1) and (2), we get

→EA=−2→EB

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