Q. 223.9( 7 Votes )

# An electron gun w

Answer :

Given:

Potential at collector, V = 100V

Magnetic field strength, B = 2.83 × 10^{-4} T

Radius of orbit traced by electron, r = 12.0 cm

Let specific charge (i.e. e/m) = K

Kinetic energy of an electron is given by:

KE = = eV

→ v = …(1)

Where,

M = mass of electron

v = velocity of electron

e = charge of electron

V = potential difference (accelerating potential)

We also know that the bending is caused by the magnetic field,

So we can write,

Magnetic force = centrifugal force

e × v × B =

→ e × B =

→ v = …(2)

Where,

e = Charge on electron

v = velocity of particle

B = magnetic field strength

m = mass of electron

r = radius of trajectory

By equating (1) and (2) we can write,

.

→

By putting the values in above equation we get,

Hence the specific charge is 1.7 × 10^{-11} C Kg^{-1}.

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