Question

Two 10-cm-diameter charged disks face each other, 17 cm apart. The left disk is charged to - 50 nC and the right disk is charged to + 50 nC

By what distance has the proton been deflected sideways when it reaches the far edge of the capacitor? Assume the field is uniform inside the capacitor and zero outside the capacitor.

Answer 1

given

Q = 50 nC = 50*10^-9 C

Area of each plate, A = pi*d^2/4

= pi*0.1^2/4

= 0.00785 m^2

eletric field between the plates,

E = Q/(A*epsilon)

= 50*10^-9/(0.00785*8.854*10^-12)

= 7.19*10^5 N/c

acceleration of proton in y-direction,

ay = q*E/m

= 1.6*10^-19*7.19*10^5/(1.67*10^-27)

= 6.89*10^13 m/s^2

time taken for the proton to cross the plates,

t = d/vox

= 0.1/vox

substitute initial velocity of proton in the above equation and get t.

then use the follwing equation,

so, deflection in y direction, delta_y = (1/2)*ay*t^2

= (1/2)*6.89*10^13*t^2

= ..... m