InterviewSolution
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InterviewSolution
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(a) Define electric dipole moment. Is it a scalar or a vector ? Derive the expression for the electric field of a dipole at a point on theequatorial plane of the dipole. (b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero. |
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Answer» Solution :(a) Electric dipole MOMENT : The strength of an electric dipole is measured by the quantity electric dipole moment. Its magnitude is equal to the product of the magnitude of either charge and the distance between the two charges. Electric dipole moment, `p = q xx d` It is a vector quantity. In vector form, it is written as `vec(p)=q xx vec(d)`, where the direction of `vec(d)` is form negative charge to positive charge. Electric field of dipole at points on the equatorial PLANE : The magnitude of the electric field due to two charges + q and -q are given by `E_(+q)=(q)/(4pi E_(0))(1)/(r^(2)+a^(2))""...(i)` `E_(-q)=(q)/(4pi E_(0))(1)/(r^(2)+a^(2))""...(ii)` `therefore""E_(+q) = E_(-q)` The direction of `E_(+q) and E_(-q)` are SHOWN in figure :  The COMPONENTS normal to the dipole axis cancel away. The components along the dipole axis add up. `therefore` Total electric field `E=-(E+(+q)+E_(-q))cos theta hat(p) rArr E =-(2qa)/(4 pi in_(0)(r^(2)+a^(2))^(3//2))hat(p)""...(iii)` At large distance `(r gt gt a)`, this reduce to `E = -(2qa)/(4 pi in_(0)r^(3))hat(p)""...(iv)` `vec(P)=q xx 2 vec(a) hat(p)` `E = (-vec(p))/(4 pi in_(0)r^(3))(r gt gt a)` (b) Potential at all points in equatorial plane is zero everywhere `V_(net) = V_(A) + V_(B)` `=(-Kq)/((r^(2)+a^(2)))+(Kq)/((r^(2)+a^(2)))=0` 
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