1.

When an electric dipole of moment `| vec(p) | = q xx 2a` is held at an angle `theta`, with the direction of uniform external electric field `vec(E)`, a torque `tau = pE sin theta` acts on the dipole. This torque tries to align the electric dipole in the direction of the field. When `vec(p)` is along `vec(E), theta^(@) , tau = pE sin 0^(@) = zero`. The dipole is in stabel equilibrium. The energy possessed by the dipole by 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, `theta 0^(@), :. U = -pE` = minimum. Read the above passage and answer the following questions : (i) What is the direction of torque acting on electric dipole held at an angle with uniform external electric field ? (ii) An electric dipole of length 10cm having charges `+- 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 physical significance of this concept in our day to day life ?

Answer» (i) `tau = pE sin theta` can be rewritten in vector form as : `vec(tau) = vec(p) xx vec(E)`
Therefore, the direction of torque `vec(tau)` is perpendicular to both `vec(p) and vec(E)`. It is determined by right handed screw rule.
(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 sin theta`
`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 electric dipole held in an external field will be in stable equilibrium only when it is aligned along the field and it possesses minimum potential energy. The same is 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 aligned and your persnal whims are at lowest ebb.


Discussion

No Comment Found

Related InterviewSolutions