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A charged particle is moving in a circular orbit of radius $6\, cm$ with a uniform speed of $3 \times 10^6\, m/s$ under the action of a uniform magnetic field $2 \times 10^{-4}\, Wb/m^2$ which is at right angles to the plane of the orbit. The charge to mass ratio of the particle is
$5 \times {10^9}\,C/kg$
$2.5 \times {10^{11}}\,C/kg$
$5 \times {10^{11}}\,C/kg$
$5 \times {10^{12}}\,C/kg$
Solution
Here, $\mathrm{v}=3 \times 10^{6}\, \mathrm{ms}^{-1}$
$B=2 \times 10^{-4} \,\mathrm{Wb} \mathrm{m}^{-2}=2 \times 10^{-4} \,\mathrm{T}$
$\mathrm{R}=6\, \mathrm{cm}=6 \times 10^{-2} \,\mathrm{m}$
$\mathrm{As}, \mathrm{Bqv}=\frac{\mathrm{mv}^{2}}{\mathrm{R}}$ or $\frac{\mathrm{q}}{\mathrm{m}}=\frac{\mathrm{v}}{\mathrm{BR}}$
Substituting the given values, we get;
$\frac{\mathrm{q}}{\mathrm{m}}=\frac{3 \times 10^{6}}{2 \times 10^{-4} \times 6 \times 10^{-2}}=2.5 \times 10^{11}\, \mathrm{C} / \mathrm{kg}$
