Question

A charged particle is moving in a circular path in uniform magnetic field with speed v. Match the following

Answer 1

We know,

$R=\frac{mv}{qB}$

$R\propto v$

$\text{Case A}$

$I=q\omega =\frac{q\times 2\pi R}{v}$

$I=\frac{q\times 2\pi mv}{qBv}$

$I\propto v^0$

$A\to 3$

$\text{Case B}$

Magnetic Moment$=I\pi R^2$

$=\frac{2\pi m\times m^2{v}^2}{q^2{B}^3}$

$B\to 2$

$\text{Case C}$

$B^{\prime }=\frac{{\mu }_{0}I}{2\pi R}$

$B^{\prime }=\frac{{\mu }_0}{2\pi }\times \frac{2\pi m\times qB}{B\times mv}$

$B^{\prime }\propto v^{-1}$

$C\to 4$

$\text{Case D}$

$R=\frac{mv}{qB}$

$R\propto v$

$D\to 1$