Question

A parallel-plate capacitor has 4.6 cm × 4.6 cm electrodes with surface charge densities ±1.0×10−6C/m2. A proton traveling parallel to the electrodes at 2.0×10⁶ m/s enters the center of the gap between them.

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

Force, F = ma = qσ/mε_o

Acceleration, a = (1.6 x 10^-19 x 10^-6)/(8.85 x 10^-12 x 1.67 x 10^-27) = 1.08 x 10^13 m/s^2

Time, t = d/v = 0.046/(2 x 10^6) = 2.3 x 10^-8 sec

Deflection, d = 0.5 at^2

d = 0.5 x 1.08 x 10^13 x (2.3 x 10^-8)^2 = 2.86 x 10^-3 m

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