A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2 imes10^5\ \mathrm{m\,s^{-1}}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x imes10^4$ N/C. The value of $x$ is _______ Take the mass of the proton $=1.6 imes10^{-27}$ kg.

Question

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2	imes10^5\ \mathrm{m\,s^{-1}}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x	imes10^4$ N/C. The value of $x$ is _______ Take the mass of the proton $=1.6	imes10^{-27}$ kg.

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] With the electric field off, $r=\frac{mv}{eB}$, so $B=\frac{1.6	imes10^{-27}	imes2	imes10^5}{1.6	imes10^{-19}	imes0.02}=0.1$ T. Undeflected motion needs $E=vB=2	imes10^5	imes0.1=2	imes10^4$ N/C, so $x=2$. Answer: 2.

Explanation

Reviewed by Dr. Abubacker

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