A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2 imes 10^5 \mathrm{~ms}^{-1}$. 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 imes 10^4 \mathrm{~N}…

Question

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2 	imes 10^5 \mathrm{~ms}^{-1}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x 	imes 10^4 \mathrm{~N} / \mathrm{C}$. The value of $x$ is _______ Take the mass of the proton $=1.6 	imes 10^{-27} \mathrm{~kg}$.

Aicharya · Accepted Answer

$\begin{aligned} & B v q=E q \ & E=B v \ & r=\frac{v m}{B q} \ & B=\frac{m v}{r q} \ & E=\left(\frac{m v}{r q}ight) v=\frac{m v^2}{r q} \ & =\frac{1.6 	imes 10^{-27} 	imes 4 	imes 10^{10}}{2 	imes 10^{-2} 	imes 1.6 	imes 10^{-19}} \ & =2 	imes 10^4 \mathrm{~N} / \mathrm{C} \ & x=2\end{aligned}$

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2…

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