Subject: Applied Physics 2

Topic: Motion Of Charged Paqrticle In Electric And Magnetic Field

Difficulty: Medium

Magnetic field of $10^{-4} Wb/m^2$ acts over a length of 3 cm in a given region. The distance from the centre of the field to the screen is 20 cm. If the accelerating voltage is 800V, calculate the electron beam deflection on the screen. Also find the displacement of a particle with charge twice that of an electron & mass 7344 times as large. Given: e/m = $1.76 \times 10^{11}$ C/kg.

$$ $$ $B =10^-4 Wb/m^2 \\ l = 3 cm, \\ d = 20 cm. \\ V_A = 800 V,\\ Deflection =?, \\ $

$\text{Charge of an electron }1.6 *10^{-19} \\ $

$ \text{Mass of an electron } 9.1*10^{-31} \\ $

$ Deflection Y = DlB √(e/(2mVA )) \\ $

$ Y = 20 * 10^-2 * 3 * 10^-2 *1 x 10^-4 √(( 1.6 *10^{-19})/(2 * 9.1 * 10^{-31}*800 )) \\ $

$ Y = 6.3 mm \\ $

$ \text{For the charge with charge twice that of electron and mass 7344 times.} \\ $

$ \text{Deflection Y = DlB √(2e / (2x 7344 mVA ))} \\ $

$Y = 20*10^-2 * 3 * 10^-2 *1 * 10^-4 √( ( 1.6 *10^{-19} *2) / (2*7344 *9.1 *10^{-31} *800 )) \\$ $ Displacement = 0.01 cm \ $