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Class 12 › Physics › Moving Charges and Magnetism
CBSE2023Class Class 12 · Physics1 Marks · Long✅ Verified
Case Study (Charged particles): Particle 1 (mass $m$, charge $-q$) and particle 2 (mass $\frac{m}{2}$, charge $+2q$) accelerated through the same $V$, then enter a magnetic field $B$ perpendicular to velocity. Q: The ratio of the radii of their circular paths $\left(\dfrac{r_1}{r_2}\right)$ is:
✅ Answer & Solution
Radius in a magnetic field: $$r = \frac{mv}{qB} = \frac{\sqrt{2mK}}{qB} = \frac{\sqrt{2m(qV)}}{qB} = \frac{1}{B}\sqrt{\frac{2mV}{q}}$$ So $r \propto \sqrt{\dfrac{m}{q}}$ (with V, B common). For particle 1: $r_1 \propto \sqrt{m/q}$. For particle 2: $r_2 \propto \sqrt{(m/2)/(2q)} = \sqrt{m/4q} = \frac{1}{2}\sqrt{m/q}$. $$\frac{r_1}{r_2} = \frac{\sqrt{m/q}}{\frac12\sqrt{m/q}} = 2$$ Hence the correct option is (D).
