Q 1. An electric dipole with dipole moment 4 x 10 -9 Cm is aligned at 30O with direction of a uniform electric field of magnitude 5 x 10 4 N/C. calculate the magnitude of torque acting on the dipole.
Total charge of the system is zero . Dipole moment of system is given by q x d =7.5x 10-8 Cm
Q 2. A system has two charges qA = 2.5 x 10 -7 C and qB = -2.5 x 10 -7 C are located at points A(0,0,-15 cm) and B(0,0,+15 cm) respectively. What are the charge and electric dipole moment of the system?
Torque =pE Sin θ =10-4 Nm
Q 3. In a certain region of space, electric field is along the z direction throughout. The magnitude of electric field, however not constant but increases uniformly along the positive z direction, at the rate of 10 5 N/C/m. What are the force and torque experienced by a system having a total dipole moment equal to 10-7 Cm in the negative z-direction?
Force along the – ve Z axis 10-2 N Torque = pE sin 180O = 0
Q 4. An dipole of length 2 cm is placed 300 w.r.t a uniform electric field of 105 N/C experiences a torque of magnitude 10√3 Nm. Calculate (i) magnitude of charge and (ii) PE of electric dipole.
i)√3 x 10-2 C (ii) U = -30 J.
Q5. An electric dipole consist of two opposite charges of magnitude q=1 x 10 -6 C separated by 2 cm. The dipole is placed in an external field of 1 x 10 5 N/C.What maximum torque does the field exert on the dipole? How much work must an external agent do to turn the dipole end for end, starting from position of alignment (θ=0O)?
2 x 10-3 Nm is max torque and work done
Q6. An electric dipole consist of charges +2 e and -2 e separated by 0.78 nm. It is an electric field of strength 3.4 x 106 N/C. Calculate the magnitude of the torque on the dipole when the dipole moment is
i) Parallel to
ii) Perpendicular to
iii) Antiparallel to electric field
(i) Zero (ii) 8.5 x 10-22 Nm (iii) Zero
Q7.An electric dipole of length 10 cm having charges ±6 x 10 -3C, placed at 30O with respect to a uniform electric field experiences a torque of magnitude 6(3)1/2 Nm. Calculate
i) Magnitude of electric field
ii) Potential energy of dipole.
(i)E = 2 √3x104N/C (ii)U = -18 J
Q8.An electric dipole of length 4 cm, when placed with its axis making an angle of 60◦ with a uniform electric field experiences a torque of 4(3)1/2 Nm. Calculate the potential energy of the dipole, if it has charge of ± 8 nC.