Q12 of 31 Page 169

In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

Given:


Magnetic field strength, B = 6.5 G = 6.5 × 10-4 T


Initial velocity of electron = 4.8 × 106 ms-1


Angle between the initial velocity of electron and magnetic field, θ = 900


We can relate the velocity of the electron to its angular frequency by the relation,


V = rω …(1)


Where,


V = velocity of electron


r = radius of path


ω = angular frequency



We understand that, magnetic force on the electron is equal to the centripetal force on it, hence we can write,


Fe = Fc


e × V × B = mV2/r …(2)


From equation (2) we can write,


⇒ eB = mV/r …(3)


Now, by putting value of V from equation (1) in equation (3)



⇒ e × B = m × ω …(4)


We know that, ω = 2πν


Putting in equation (4), we have


…(5)


Now, by putting the values in equation (5) we get,


⇒


⇒ v = 18.2 × 106Hz


Hence, the frequency of rotation is 18.2 × 106Hz.


Note: The frequency of rotation is independent of the initial velocity of the electron.


More from this chapter

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10

Two moving coil meters, M1 and M2 have the following particulars:

R1 = 10Ω, N1 = 30,


A1 = 3.6 × 10–3 m2, B1 = 0.25 T


R2 = 14Ω, N2 = 42,


A2 = 1.8 × 10–3 m2, B2 = 0.50 T


(The spring constants are identical for the two meters).


Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M2 and M1.

 11

In a chamber, a uniform magnetic field of 6.5 G (1 G = 10–4 T) is maintained. An electron is shot into the field with a speed of 4.8 × 106 m s–1 normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e = 1.5 × 10–19 C, me = 9.1 × 10–31 kg)

 13

A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of 60° with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.

 13

Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)