CBSE Class 12-science Answered
Derive an expression for work in rotating dipole use it to find formula for energy of the dipole. What is the stable position of dipole in the field?
Asked by 342849142950171 | 01 Oct, 2018, 01:13: AM
Expert Answer
Let a dipole is placed in a uniform field of intensity E and dipole vector makes an angle θ with field direction.
Positive charge experiences a force qE in the field direction. Negative charge experiences a force -qE in opposite direction.
Though net force is zero,two forces separated by a distance making a couple.
Torque τ of the couple is product of force and perpendicular distance between them.
Torque τ = qE×2a×sinθ ...................(1)
but we know that q×2a is dipole moment p, hence torque τ = p×E×sinθ ........................(2)
since τ, p and E are vector quantities, eqn.(2) is expressed as cross product or vector poroduct, τ = p × E
Workdone W to turn the dipole from angular position θ0 to θ1 is given by, W = 
By convention, θ0 is taken as π/2 (reference point, point of minimum potential energy ), hence W = - p E cosθ ...............(3)
eqn(3) can be written in scalar product or dot product of vectors as W = - p · E
dipole is stable, when it is aligned in the direction of electric field
Answered by Thiyagarajan K | 03 Oct, 2018, 06:54: PM
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