Question

27. A dipole consists of two opposite charges (q E and q) separated by a fixed distance d. The dipole is placed in an electric field in the +a-direction of magnitude E. The dipole axis makes an angle θ with the electric field as shown in Figure 1.10. +x -q Figure 1.10: an electric dipole in an electric field E (a) Calculate the net electric force acting orn the dipole. (b) Calculate the net torque acting on the dipole due to the electric forces as a func- tion of θ. Let counterclockwise torque be positive. 0°, 36.9°, 7.0 cm, (c) Evaluate the net torque for θ and 90.00. Let q 3.0 10, d and E= 2.0 × 104 N/C.

Can someone please answer in detialed steps with explantion. (thank you!)

Answer 1

(a) The net electric force acting on the dipole is Sigma f_x = q E_x - q E_x = 0 Sigma F_y = q E_y - q E_y = q (0) - q (0) = 0 F_net = 0 (b) the net torque on the dipole is Sigma T = -F_-q r_-q sin theta - F_2 r_q sin theta = -q E [d/2] sin theta - q E [d/2] sin theta = -q E d sin theta (c) the net torque for each angle theta T (0) = -(3 times 10^-6 c) (2 times 10^4 N/c) (0.070) sin theta Sigma T (0) = -(3 times 10^-6 C) (2 times 10^4 N/c) (0.070) sin (0) Sigma T (36.9) = -(3 times 10^-6) (2 times 10^4) (0.070) sin (36.9 degree) = -0.0025 N - m Sigma T (90) = -(3 times 10^-6) (2 times 10^4) (0.070) sin (90 degree) = -0.0042 N - m