An electron gun is placed inside a long solenoid of radius $$R$$ on its axis. The solenoid has $$n$$ turns/length and carries a current $$I$$. The electron gun shoots an electron along the radius of the solenoid with speed $$v$$. If the electron does not hit the surface of the solenoid, maximum possible value of $$v$$ is (all symbols have their standard meaning):

A

$$\frac{e\mu_0 nIR}{m}$$

B

$$\frac{e\mu_0 nIR}{2m}$$

C

$$\frac{e\mu_0 nIR}{4m}$$

D

$$\frac{2e\mu_0 nIR}{m}$$