A proton is fired through a capacitor toward a target at 5.0 times 10^5 m/s. The

Question

A proton is fired through a capacitor toward a target at 5.0 times 10^5 m/s. The capacitor is made up of 2 square plates 10 cm on a side, with an electric field of 1.0 times 10^4 N/C between the plates, directed downward. The target is centered between the plates but just outside them. The mass of a proton is m_p = 1.67 times 10^-27 kg. a) In order to hit the target, should the proton be fired above or below the center of the plates? b) How far above or below the center of the plates should the proton be fired in order to hit the center of the target?

Explanation / Answer

Here ,

a) as the force on the proton will be downwards , it shall be fired above the centre of plates

b)

time taken for proton to hit the target , t = 0.10/(5*10^5 ) s

t = 2 *10^-7 s

Now, let the acceleration of proton is a

1.67 *10^-27 * a = 1.602 *10^-19 * 1 *10^4

solving for a

a = 9.57 *10^11 m/s^2

distance above centre = 0.5 * a * t^2

distance above centre = 0.50 * 9.57 *10^11 * (2 *10^-7)^2

distance above centre = 0.0191 m = 1.91 cm

the distance above centre is 1.91 cm

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