An electric dipole consists of two equal and opposite charges situated a very small distance from each other. When the dipole is placed in a uniform electric field, which of the following statements is true? a) The dipole will not experience any net force from the electric field; since the charges are equal and have opposite signs, the individual effects will cancel out. b) There will be no net force and no net torque acting on the dipole. c) There will be a net force but no net torque acting on the dipole. d) There will be no net force, but there will (in general) be a net torque acting on dipole.

Short Answer

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(a) There will always be a net force and torque acting on the dipole; (b) There will never be a net force or torque acting on the dipole; (c) There will always be a net force and sometimes a net torque acting on the dipole; (d) There will be no net force, but there will (in general) be a net torque acting on the dipole. Answer: (d) There will be no net force, but there will (in general) be a net torque acting on the dipole.

Step by step solution

01

Understanding Electric Dipole

An electric dipole consists of two equal and opposite charges placed at a very small distance from each other. In a uniform electric field, each charge will experience a force proportional to the product of the charge and the electric field. The force on the positive charge will act in the direction of the field, while the force on the negative charge will act in the opposite direction.
02

Net Force Acting on the Dipole

Since the charges are equal and opposite, and the electric field is uniform, the magnitude of the forces acting on each charge due to the electric field will be the same. However, these forces will be acting in opposite directions, thus they will cancel each other out and the net force on the dipole will be zero.
03

Net Torque Acting on the Dipole

To determine the net torque acting on the dipole, we need to calculate the torque due to the forces acting on each charge. Torque (\tau) is the cross product of the position vector (r) and the force vector (F): \tau = r \times F. Since the forces are acting at opposite ends of the dipole and in opposite directions, they will produce a torque in the same direction, causing the dipole to rotate. In general, if the dipole is not aligned with the electric field, there will be a net torque acting on it. However, when the dipole is aligned with (or in the opposite direction of) the electric field, the net torque will be zero. Based on the analysis of net force and net torque, the correct answer is: d) There will be no net force, but there will (in general) be a net torque acting on the dipole.

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