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Physics Question on Moving charges and magnetism

A 10 eV10\ eV electron is circulating in a plane at right angles to a uniform field at magnetic induction 10−4 Wb/m2{10}^{- 4}\ Wb/m^2 (= 1.01.0 gauss), the orbital radius of electron is

A

11 cm

B

18 cm

C

12 cm

D

16 cm

Answer

11 cm

Explanation

Solution

Kinetic energy of electron (12×mv2)=10 eV\bigg( \frac{1}{2} \times m v^2 \bigg) = 10 \,eV
and magnetic induction (B) = 10−4Wb/m2{10}^{-4} Wb / m^2
Therefore 12(9.1×10−31)v2=10×(1.6×10−19)\frac{ 1}{2} (9.1 \times {10}^{-31}) v^2 = 10 \times (1.6 \times {10}^{-19})

or, v2=2×10×(1.6×10−19)9.1×10−31=3.52×1012v^2 = \frac{ 2 \times 10 \times (1.6 \times {10}^{-19})}{ 9.1 \times {10}^{-31}} = 3.52 \times {10}^{12}

or , v=1.876×106 mv= 1.876 \times {10}^6 \,m.

Centripetal force = mv2r=Bev.\frac{ m v^2}{r} = Bev .

Therefore r=mvBe=(9.1×10−31)×(1.876×106)10−4×(1.6×10−19)r= \frac{ mv}{Be} = \frac{ (9.1 \times {10}^{-31}) \times (1.876 \times {10}^6)}{ {10}^{-4} \times (1.6 \times {10}^{-19})}
=11×10−2m= 11 \times {10}^{-2} m
=11 cm= 11\, cm.

So, the correct option is (A): 11 cm