Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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A Circular Loop of Radius 20 Cm Carries a Current of 10 A. an Electron Crosses the Plane of the Loop with a Speed of 2.0 × 106 M S−1. - Physics

Short Note

A circular loop of radius 20 cm carries a current of 10 A. An electron crosses the plane of the loop with a speed of 2.0 × 106 m s−1. The direction of motion makes an angle of 30° with the axis of the circle and passes through its centre. Find the magnitude of the magnetic force on the electron at the instant it crosses the plane.

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Solution

Given:
Magnitude of current in the loop, I = 10 A
Radius of the loop, r = 20 cm = 20 × 10−2 m
Thus, the magnetic field intensity at the centre is given by \[B = \frac{\mu_0 I}{2r}\]

Now,
Velocity of the electron, v = 2 × 106 m/s
Angle between the velocity and the magnetic field intensity, θ = 30°
Thus, the magnetic force on the electron is given by

\[F   =   evB\sin  \theta\] 

\[ = 1 . 6   \times  {10}^{- 19}  \times 2 \times  {10}^6  \times \frac{\mu_0 i}{2R}\sin  30^\circ \] 

\[ =   1 . 6 \times  {10}^{- 19}  \times 2 \times  {10}^6  \times \frac{4\pi \times {10}^{- 7} \times 10}{2 \times 20 \times {10}^{- 2}} \times \frac{1}{2}\] 

\[ = 16\pi \times  {10}^{- 19} \] N

Concept: Magnetic Field on the Axis of a Circular Current Loop
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 13 Magnetic Field due to a Current
Q 38 | Page 252
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