Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismMagnetic ForceEasy2 minPYQ_2020

PhysicsEasysingle choice

An electron and a proton have equal kinetic energies. They enter in a magnetic field perpendicular to $B,$ then

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Answer:

Solution:

For such a motion, magnetic force = centripetal force

$q v B = \frac{m v^{2}}{r}$

$\Rightarrow q B = \frac{m v}{r}$

$\Rightarrow r = \frac{m v}{q B}$

$∴ \frac{r_{p}}{r_{c}} = \frac{m_{p} v_{p}}{q B} \times \frac{q B}{m_{e} v_{e}}$

but $K_{e} = K_{p}$ (given)

$\Rightarrow \frac{1}{2} m_{e} v_{e}^{2} = \frac{1}{2} m_{p} v_{p}^{2}$

$\Rightarrow \frac{m_{p}}{m_{e}} = {(\frac{v_{e}}{v_{p}})}^{2}$

$∴ \frac{r_{p}}{r_{e}} = {(\frac{v_{e}}{v_{p}})}^{2} \frac{v_{p}}{v_{e}} = \frac{v_{e}}{v_{p}}$

Hence, the electron and proton will follow circular paths but with different radii.

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:MagnetismSubtopic:Magnetic Force

⏱ 2mℹ️ Source: PYQ_2020

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