Circular Motion In A Magnetic Field

Question

An electron travels in a circular path of radius $r$ inside a uniform magnetic field; if its speed is doubled while the field is kept unchanged, the new radius of its circular path becomes

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When a charged particle moves perpendicular to a uniform magnetic field, the magnetic force provides the centripetal force needed for circular motion, as described in NCERT Class 12, Chapter 4 (Moving Charges and Magnetism). Setting the Lorentz force equal to the centripetal force: $qvB = \dfrac{mv^{2}}{r}$, which rearranges to $r = \dfrac{mv}{qB}$. This shows the radius is directly proportional to the speed when charge, mass, and field are constant. Therefore, doubling the speed doubles the radius, giving a new radius of $2r$. The option $r/2$ inverts the proportionality and is incorrect. The option $4r$ mistakenly treats radius as proportional to $v^{2}$, which would be true for kinetic energy but not for radius. The option $r$ ignores the dependence on speed entirely. Plausibility check: dimensionally $\dfrac{mv}{qB}$ gives $\dfrac{	ext{kg}\cdot 	ext{m/s}}{	ext{C}\cdot 	ext{T}} = 	ext{m}$, confirming a length, and a faster particle logically sweeps a wider circle since it resists being turned more strongly.

Circular Motion In A Magnetic Field

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Circular Motion In A Magnetic Field

Select the correct option:

🔒 Solution Hidden from View

More magnetic effects of current and magnetism Practice Questions

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About This Question

Solution

The magnetic susceptibility of a paramagnetic sample is measured as $0.006$ at a temperature of $300...

In a region with a uniform electric field of $3 \times 1 0^{4}$ V/m perpendicular to a magnetic field...

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A galvanometer of resistance $50 Ω$ shows full-scale deflection at $2$ mA; what shunt resistan...

A rectangular coil of $50$ turns and area $2 \times 1 0^{- 2}$ m $^{2}$ carries a current of $1.5$ A whil...

To convert a galvanometer of resistance $60 Ω$ and full-scale current $5$ mA into a voltmeter ...

A bar magnet of magnetic moment $0.8$ A·m $^{2}$ is held at $3 0^{\circ}$ to a uniform magnetic field of...