An electron gun is placed inside a long solen | vedclass

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Question

(B) The magnetic field inside a long solenoid is $B = \mu_{0} nI$. When an electron is projected radially with speed $v$,it experiences a Lorentz forc

Vedclass · Accepted Answer

$\frac{e \mu_{0} nIR}{2 m}$

Vedclass · Answer

(B) The magnetic field inside a long solenoid is $B = \mu_{0} nI$. When an electron is projected radially with speed $v$,it experiences a Lorentz force $F = evB$ perpendicular to its velocity,causing it to move in a circular path of radius $r = \frac{mv}{eB}$.For the electron not to hit the surface of the solenoid of radius $R$,the diameter of its circular path must be less than or equal to the radius of the solenoid. Thus,$2r \leq R$,which implies $r \leq \frac{R}{2}$.Substituting $r = \frac{mv}{e(\mu_{0} nI)}$,we get $\frac{mv}{e\mu_{0} nI} \leq \frac{R}{2}$.Therefore,the maximum speed $v_{\max}$ is $\frac{e \mu_{0} nIR}{2m}$.

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