Question

$find \: the \: force \: experienced \: by \\ the \: proton \: and \: also \: the \\ direction \: of \: force \: with \: complete \\ explaination$

Answer 1

Magneti field due to a current carrying wire at a distance r is given as:

$B = \frac{ \mu_o I}{2 \pi r}$

By right hand thumb rule, we know that this will act into the paper near proton.

lets say velocity of proton = v (in downward direction)

So angle between direction of motion of proton and magnetic fields is 90°.

Force on a charge 'q' moving at velocity 'v' due to magnetic field 'B' is given as

$force = qvB \sin( \theta) \\ \\ q = e \\ v = v \\ B = \frac{ \mu_{o}I}{2\pi r} \\ \\ F= ev \times \frac{ \mu_{o}I}{2\pi r} \times \sin(90) \\ \\ F = ev \times \frac{ \mu_{o}I}{2\pi r} \times 1 \\ \\ F = \frac{ \mu_{o}Iev}{2\pi r}$

The direction of force can be found out by Right Hand Rule.

If you keep thumb along V, index finger along B then middle finger will give the direction of force.

So force is towards right in the plane of the paper.

Answer 2

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