Force and Torque on Dipole
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Exercise:
Find the net force and torque acting on an electric dipole in a uniform electric field. center includegraphicswidthtextwidth#image_path:dipolforctorqu# center
Solution:
The forces acting on the positive and negative charge of the dipole are equal in magnitude but opposite in direction see figure. center includegraphicswidthtextwidth#image_path:dipolforctorquwith-forces-# center The net force is therefore sscFnet F_+ - F_- The torque caused by the force acting on the positive charge with respect to the midpoin M is tau_+ F_+ fracd sheta The torque caused by the force acting on the negative charge has the same magnitude and acts in the same direction for the example in the figure: clockwise so the net torque is tau tau_+ F_+ d sheta q E d sheta With the electric dipole moment pqd this can be written as tau p E sheta The torque can also be defined as the cross product vectau vecpcrossvecE The direction of this vector is related to the orientation of the torque with the following right-hand rule: When the thumb of the right hand pos in the direction of vectau the fingers define the orientation of the torque.
Find the net force and torque acting on an electric dipole in a uniform electric field. center includegraphicswidthtextwidth#image_path:dipolforctorqu# center
Solution:
The forces acting on the positive and negative charge of the dipole are equal in magnitude but opposite in direction see figure. center includegraphicswidthtextwidth#image_path:dipolforctorquwith-forces-# center The net force is therefore sscFnet F_+ - F_- The torque caused by the force acting on the positive charge with respect to the midpoin M is tau_+ F_+ fracd sheta The torque caused by the force acting on the negative charge has the same magnitude and acts in the same direction for the example in the figure: clockwise so the net torque is tau tau_+ F_+ d sheta q E d sheta With the electric dipole moment pqd this can be written as tau p E sheta The torque can also be defined as the cross product vectau vecpcrossvecE The direction of this vector is related to the orientation of the torque with the following right-hand rule: When the thumb of the right hand pos in the direction of vectau the fingers define the orientation of the torque.