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A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius(r). Which of the following curves represents the variation of r with E?
$$qvB = \frac{mv^2}{r}$$
$$r = \frac{mv}{qB}$$
$$E = \frac{1}{2}mv^2 \implies v = \sqrt{\frac{2E}{m}}$$
$$r = \frac{m}{qB} \sqrt{\frac{2E}{m}}$$
$$r = \frac{\sqrt{2mE}}{qB}$$
$$r \propto \sqrt{E}$$
Graph D correctly represents the $$r \propto \sqrt{E}$$ curve.
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