Question

Two identical bar magnets are fixed with their centres at a distance $d$ apart. $A$ stationary charge $Q$ is placed at $P$ in between the gap of the two magnets at a distance $D$ from the centre $O$ as shown in the figure. The force on the charge $Q$ is

• A. zero
• B. directed along $OP$
• C. directed along $PQ$
• D. directed perpendicular to the plane of paper

Answer 1

The Correct Option is A

To determine the force on a stationary charge \( Q \) placed between two identical bar magnets, we need to consider the magnetic field and the force exerted on a charge by a magnetic field. According to the principles of electromagnetism, the force on a stationary charge in a magnetic field is given by:

• The magnetic force \( \vec{F} \) on a stationary charge in a magnetic field is zero. This is because the magnetic force on a charge is described by the equation \( \vec{F} = q(\vec{v} \times \vec{B}) \), where:
  • q is the electric charge.
  • \vec{v} is the velocity of the charge.
  • \vec{B} is the magnetic field.

Since the charge \( Q \) is stationary (i.e., its velocity \(\vec{v} = 0\)), there will be no force due to the magnetic field, as the cross product \( \vec{v} \times \vec{B} = 0 \). Therefore, the force on the charge \( Q \) is zero.

Let us assess the options given:

• Zero: Since the charge is stationary, the magnetic force is indeed zero. This is the correct option.
• Directed along \( OP \): This would imply there is a net force acting in that direction, which contradicts the condition of the charge being stationary in a magnetic field.
• Directed along \( PQ \): Similar to the previous point, there is no net force acting along \( PQ \).
• Directed perpendicular to the plane of paper: This option would imply a non-zero force in such a direction, which is not possible for a stationary charge in a magnetic field.

Hence, the correct answer is zero.