When an electric dipole of moment | vec(p) | = q xx 2a is held at an angle theta, with the direction of uniform externalelectricfield vec(E), a torquetau = pE sin theta acts on the dipole. This torquetries to align the electric dipole in the direction of the field. Whenvec(p) is alongvec(E), theta^(@) , tau= pE sin 0^(@) = zero. The dipole is in stabel equilibrium. The energy possessed by the dipoleby virtue of its particular position in the electric field is called potential energy of dipole. U = W = -pE (cos theta_(2) - cos theta_(1)) theta_(1) = 90^(@) is the position of zero potential energy. :. U = W = -pE (cos theta - cos 90^(@)) = -pE cos theta.For stable equillibrium, theta0^(@), :. U = -pE = minimum. Read the abovepassageand answer the followingquestions : (i) What is the directionof torqueacting on electric dipoleheld at an angle with uniform external electric field ? (ii) An electricdipole of length10cmhavingcharges +- 6xx10^(-3) C,placed at 30^(@) with respect to a uniform electric field experiences a torque of magnitude 6 sqrt(3) N-m. Calculate. (a) magnitude of electric field. (b) potential energy of dipole. (iii) What is the physicalsignificance of this concept in our day to day life ?

When an electric dipole of moment | vec(p) | = q xx 2a is held at an a

1.	When an electric dipole of moment \| vec(p) \| = q xx 2a is held at an angle theta, with the direction of uniform externalelectricfield vec(E), a torquetau = pE sin theta acts on the dipole. This torquetries to align the electric dipole in the direction of the field. Whenvec(p) is alongvec(E), theta^(@) , tau= pE sin 0^(@) = zero. The dipole is in stabel equilibrium. The energy possessed by the dipoleby virtue of its particular position in the electric field is called potential energy of dipole. U = W = -pE (cos theta_(2) - cos theta_(1)) theta_(1) = 90^(@) is the position of zero potential energy. :. U = W = -pE (cos theta - cos 90^(@)) = -pE cos theta.For stable equillibrium, theta0^(@), :. U = -pE = minimum. Read the abovepassageand answer the followingquestions : (i) What is the directionof torqueacting on electric dipoleheld at an angle with uniform external electric field ? (ii) An electricdipole of length10cmhavingcharges +- 6xx10^(-3) C,placed at 30^(@) with respect to a uniform electric field experiences a torque of magnitude 6 sqrt(3) N-m. Calculate. (a) magnitude of electric field. (b) potential energy of dipole. (iii) What is the physicalsignificance of this concept in our day to day life ?
Answer» Solution :(i) `tau = PE sin theta` can berewritten in vector form as : `vec(tau) = vec(p) xx vec(E)` Therefore, the directionof torque `vec(tau)`is PERPENDICULAR to both `vec(p) andvec(E)`. It is determined by RIGHT handed screwrule. (ii) Here, `2a = 10 cm = 10^(-1)m, q = +- 6xx10^(-3) C, theta = 30^(@) tau = 6 sqrt(3) N-m = ?, U = ?` From `tau = pF sin theta = q (2a) E sintheta` `6 sqrt(3) = 6xx10^(-3) (10^(-1)) E sin 30^(@) = 6xx10^(-4) E xx (1)/(2) = 3xx10^(-4) E` `E = (6 sqrt(3))/(3xx10^(-4)) = 2 sqrt(3) xx10^(4) NC^(-1)` `U =-pE cos theta = -q (2a) E cos theta = -6xx10^(-3) (10^(-1)) (2 sqrt(3) xx10^(4)) cos 30^(@)` `= -6xx10^(-4)xx2 sqrt(3) xx10^(4) xx (sqrt(3))/(2) = -18J` (iii) From teh given paragraph, we find that electricdipole held in an externalfield will be in stable equilibrium only when it is aligned along the field and it possessesminimum potentialenergy. The sameis true in day to day life. At your work place, your boss tries always to align you along his/her plan. Your job/position is secured/stable after you are perfectly alignedand your persnal whims are at lowest ebb.

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