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Idea of Symmetry

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An infinite vertical plane of positive charge has a surface charge density µ . A metal balls of mass m and charge q is attached to a thread and tied to a point A on sheet PQ. Find the angle which AB makes with plane PQ

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Solution

the dipole moment is vector quantity as it comes from vector multiplication of magnetic field and area(both vectors) and current. a solution for the angle is we have to assume the equilibrium condition i.e. thread has made a theta angle with the sheet then t cos(theta)=mg so t=mg/cos(theta) and also tsin(theta)=f(qe) so by solving (replacing the value of tension(t) from an equation ) u will get theta=tan^-1(sigma*Q/epsilon).

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