A parallel-plate capacitor has 5.0 cm × 5.0 cm electrodes with surface charge de

Question

A parallel-plate capacitor has 5.0 cm × 5.0 cm electrodes with surface charge densities Part A 1.0 × 10-6 C/m2 . A proton traveling parallel to the electrodes at 1.4x106 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. Express your answer to two significant figures and include the appropriate units. Ay= 1 Value Units Submit equest Answer

Explanation / Answer

From Gauss's Law:

Electric field in capacitor = (charge density) / (epsilon_nought)

= (1 x 10^-6) / (8.85 x 10^-12)

= 1.12 x 10^5 N/C

Force on proton = qE = 1.6 x 10^-19 x 1.12 x 10^5 = 1.807 x 10^-13 N

Acceleration of proton = F/m = (1.807 x 10^-13) / (1.67 x 10^-27) = 1.082 x 10^13 m/s^2

Time spent passing between plate distance / speed = 0.05 / 1.4 x 10^6 = 3.57 x 10^-8 s

Displacement = ut + at^2/2

= 0 + (1.082 x 10^13) x (3.57 x 10^-8)^2 / 2

= 3.86 x 10^-3 m

= 3.86 mm

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