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An electron in a vacuum chamber is fired with a speed of 8300km/stoward a large, uniformly charged plate 75cm away. The electron reaches a closest distance of 15cm before being repelled. What is the plate’s surface charge density?

Short Answer

Expert verified

The plate’s surface charge density is2.8x10-9C/m²

Step by step solution

01

Given information and formula used

Given :

The electron is fired with a speed of : 8300km/s

Distance from the uniformly charged plate : 75cm

The electron reaches a closest distance of : 15cm

Theory used :

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

E=σ2ε0

The electron's force

F=eE=eσε0

The electron's work consists of the following:

W=Fd=deσε0d=12mv2deσε0=12mv2

02

Calculating the plate’s surface charge density 

Finding d:

d=d-d=75cm-15cm=60cm=0.6m

Finally, we locate a:

deσε0=12mv2σ=mv2ε02de=(9.11×10-31)×(8.3×106)²×(8.85×10-12)2x0.6x(1.6x10-19)=2.8x10-9C/m²

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