5:13 LTE a session.masteringphysics.com C Problem 23.51 MasteringPhysics 9 of 10

Question

5:13 LTE a session.masteringphysics.com C Problem 23.51 MasteringPhysics 9 of 10 A parallel-plate capacitor has 24 cm × 24 cm electrodes with surface charge densities ±1.0 × 10-6 C/m2. A proton traveling parallel to the electrodes at 20x10s m/s enters the center of the gap between them. Part A 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. Tillie 1 Units | = 1 Value Submit Request Answer Next

Explanation / Answer

eletric field between the plates,

E = sigma/epsilon

= 1*10^-6/(8.854*10^-12)

= 1.13*10^5 N/c

acceleration of proton in y-direction,

ay = q*E/m

= 1.6*10^-19*1.13*10^5/(1.67*10^-27)

= 1.08*10^13 m/s^2

time taken for the proton to cross the plates,

t = x/vox

= 0.024/(2*10^6)

= 1.2*10^-8 s

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

= (1/2)*1.08*10^13*(1.2*10^-8)^2

= 7.80*10^-4 m or 0.78 mm

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