Two identical bar magnets are fixed with their centres at a distance $d$ apart. A stationary charge $Q$ is pla

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:

Accepted Answer

1. **Lorentz Force Law:** The magnetic force ($\mathbf{F}$) exerted on a charge $q$ moving with velocity $\mathbf{v}$ in a magnetic field $\mathbf{B}$ is defined by the equation:
   $$ \mathbf{F} = q(\mathbf{v} 	imes \mathbf{B}) $$
   [Source 191, Eq. 4.3]
2. **Condition of the Charge:** The problem specifies that the charge $Q$ is **stationary**. This means its velocity vector $\mathbf{v} = 0$.
3. **Force Calculation:** Substituting $\mathbf{v} = 0$ into the Lorentz force equation:
   $$ \mathbf{F} = Q(0 	imes \mathbf{B}) = 0 $$
   The cross product of a zero vector with any field vector is zero.
4. **Conclusion:** A stationary electric charge does not experience any force due to a magnetic field, regardless of the strength or direction of the field produced by the bar magnets .

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