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The surface charge density on an infinite charged plane is -2.0×10-6C/m2 . A proton is shot straight away from the plane at 2.0×106m/s. How far does the proton travel before reaching its turning point?

Short Answer

Expert verified

The proton travels18cm before reaching its turning point .

Step by step solution

01

Given information and formula used

Given :

The surface charge density on the infinite charged plane : -2.0×10-6C/m2

Proton shot straight away at the speed : 2.0×106m/s

Theory used :

The Electric field owing to an infinite plane is calculated as follows:

E=σ2ε0

Newton's law :

12m((vf)2(vi)2)=qEd

02

Calculating how far the proton travels before reaching its turning point 

Due to the action of the infinite plane's electric field, this proton will come to a halt before returning. We can compute the distance it goes before turning back using conservation of energy :

12m((vf)2(vi)2)=qEdd=m((vf)2(vi)2)2qE=m((vf)2(vi)2)2q(σ/2ε0)=(1.67x10-27kg)(0-(2.0x106m/s)2)(8.854x10-12C2/N·m2)(1.6x10-19C)(2.0x10-6C/m2)d=18cm

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