Question

In: Physics

(a) calculate the magnetic field, B required to produce a deflection of 0.25 rad in Thomson’s...

(a) calculate the magnetic field, B required to produce a deflection of 0.25 rad in Thomson’s experiment, assuming the values V= 205 V, length, L = 4.9 cm, and d= 1.5 cm. (b) Find the horizontal velocity vx for this case.

Expert Solution

Datas Given

Deflection = 0.25 rad = 0.25 x 180/ =

Potential Difference V = 205 V

Length = 4.9 cm = 0.049 m

d = 1.5 cm = 0.015 m

Electric Field E = V/d = 205 / 0.015 = 13666.67 N/C

a) To find the Magnetic Field B = ?

When the particle aquires avelocity v, then the kinetic energy of the particle = 1/2mv2

ie eV = 1/2mv2

v2 = 2 e V /m = 2 x 1.6 x 10-19 x 205 / 9.1 x 10-31

= 72.08 x 1012

v = = 8.49 x 106 m/s

Now qE = qvBsin

B = E / vsin = 13666.67 / 8.49 x 106 x sin 14.33o

B = 13666.67 / 8.49 x 106 x 0.2470

B = 6517 x 10-6 T

b ) The x- component of velocity vx = v cos = 8.49 x 106 x cos 14.33o

vx = 8.49 x 106 x 0.9690 =8.23 x 106 m/s

genius_generous answered 2 years ago

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