1. An electron is accelerate from rest through 150V. The electron then enters wh

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Explanation / Answer

1.) Energy gained by the electron after that acceleration = qV = ex 150 = 1.60217662 × 10-19 x 150

= 2.40326493 x 10-17 Joules

This will be the kinetic energy of the electron = 0.5 me v2

2.40326493 x 10-17 = 0.5 x 9.10938356 × 10-31 x v2

5.276460068 x 1013 = v2

v = 7263924.606 m/s

When the electron moves with this velocity in a circle, its centrifugal acceleration will be v2/R   where R is the radius and centrifugal force will be me x v2/R

this centrifugal force should be equal to the centripetal force which is the magnetic force acting on this moving charge = qvB =evB = 1.60217662 × 10-19 x 7263924.606 x 0.5 = 5.819045087 x 10-13 N

equating both, we get :

me x v2/R =  5.819045087 x 10-13

9.10938356 × 10-31 x  7263924.6062 /R = 5.819045087 x 10-13

R = 8.25999 x 10-5 m = 0.0825999 mm

2.) Magnetic field inside a long solenoid (l>>r as in our case) is B = onI where n is the number of turns per unit length

n = 210 /0.15 = 1400

B = 4 × 107 x 1400 x 15 = 0.026389378 T

3.) The magnetic field inside a solenoid is along the axis.

And the magnetic force F = q (vxB) where v x B is the cross product between the velocity and the magnetic field B

this is given by F = qvB Sin where   is the angle between the velocity and magnetic field .

Since the proton is moving along the axis ,   is either 0 or 180 degrees. In either case, Sin = 0

So, the magnetic force on the proton is zero.

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