A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of . When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is . the value of x

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Solution

Q.
A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2 \times 10^{5} {ms}^{- 1}$ . When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x \times 10^{4} N / C$ . the value of x is ________. (Take the mass of the proton $= 1.6 \times 10^{- 27} kg$ .) [2025]

Ans.
(2)

For uniform speed : Bvq = Eq $\Rightarrow$ E = Bv

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

$E = (\frac{m v}{r q}) v = \frac{m v^{2}}{r q}$

$E = \frac{1.6 \times 10^{- 27} \times 4 \times 10^{10}}{2 \times 10^{- 2} \times 1.6 \times 10^{- 19}} = 2 \times 10^{4} N / C$

$\Rightarrow x = 2$

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