Question

An electric dipole is placed in an external uniform electric field. The net electric force on the dipole

• A. is always zero
• B. depends on the orientation of the dipole
• C. can never be zero
• D. depends on the dipole moment of the dipole

Hint:

In a uniform field the forces on +q and -q are equal and opposite, so they cancel.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
An electric dipole has two equal and opposite charges, +q and -q, a small distance apart. We are asked about the net force on it when the external electric field is the same everywhere (uniform).

Step 2: Key Formula or Approach:
The force on a charge q in a field \(\vec{E}\) is \(\vec{F} = q\vec{E}\). The net force is the vector sum of the forces on the two charges.

Step 3: Force on Each Charge:
The force on +q is \(+q\vec{E}\). The force on -q is \(-q\vec{E}\). The field is the same at both places, because it is uniform.

Step 4: Net Force:
\[ \vec{F}_{net} = q\vec{E} + (-q)\vec{E} = 0 \] The two forces are equal in size and opposite in direction, so they cancel. This holds for every orientation of the dipole. They act at different points, so they can form a torque, but the net force stays zero.

Step 5: Checking Each Option:
Option 1 says the net force is always zero. This is true for a uniform field.
Option 2 is wrong because orientation changes the torque, not the net force.
Option 3 is wrong because the net force does become zero.
Option 4 is wrong because the dipole moment \(p = q \cdot 2a\) affects the torque \(\tau = pE\sin\theta\), not the net force.

Final Answer:
The net force on a dipole in a uniform electric field is always zero, so option 1 is correct. \[ \boxed{1} \]