An electric current $^{\prime} I^{\prime}$ enters and leaves a uniform circular wire of radius $r$ through diametrically opposite points. A particle carrying a charge $q$ moves along the axis of the circular wire with speed $v$. What is the magnetic force experienced by the particle when it passes through the centre of the circle?

• A

  $q v \frac{\mu_{0} i}{a}$
• B

  $q v \frac{\mu_{0} i}{2 a}$
• C

  $q v \frac{\mu_{0} i}{2 \pi a}$
• Correct answer
  D

  Zero

Solution

Given, electric current in circular wire $=I$ Radius of wire $=r$ Charge on particle $=q$ Speed of the particle $=v$ The given loop can be as shown in the figure below. $1 / 2$ $\because$ Net magnetic field at the centre $=0$ So, magnetic force $\mathbf{F}_{\text {magnetic }}=q(\mathbf{v} \times \mathbf{B})=0$ So, the magnetic force experienced by the particle when it passes through the centre is $F=0$

Hence, the correct answer is option: 'D'.