Two 5.0 cm long parallel electrodes are spaced 1.0 cm apart. A potential differe

Question

Two 5.0 cm long parallel electrodes are spaced 1.0 cm apart. A potential difference of 500 V is applied across the electrodes. A proton enters the plates from one end halfway between the electrodes and is deflected. The proton then strikes the corner on the far end of the lower electrode. What uniform magnetic field will allow the proton to pass through undeflected while the 500 V potential difference remains applied? Assume that the magnetic field is perpendicular to the electric field and to the proton’s velocity.

Explanation / Answer

Here,

let the acceleration of proton is the a

eletric field is E = V/d

E = 500/(0.01) = 5 *10^4 V/m

let the time taken to reach the bottom is t

Using second equation of motion

d/2 = 0.5 * a * t^2

0.01/2 = 0.5 * (1.602 *10^-19 * 5 *10^4/(1.67 *10^-27)) * t^2

solving for t

t = 4.57 *10^-8 s

initial velocity of proton , u = 0.05/(4.57 *10^-8)

u = 1.09 *10^6 m/s

Now , for the magnetic field such that the proton is undeflected

magnetic field = E/u

magnetic field = 5 *10^4/(1.09 *10^6)
magnetic field = 0.0458 T

the magnetic field neded is 0.0458 T

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