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7 days ago

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At time t=0 a proton is a distance of 0.360 m from a very large insulating sheet of charge and is moving parallel to the sheet w

ith speed 960 m/s . The sheet has uniform surface charge density 2.34.×10−9C/m2 . What is the speed of the proton at 5.40

1 answer:

serg [3.4K]7 days ago

3 0

Explanation:

The formula for the electric field produced by an infinite sheet of charge is outlined below.

E = $\frac{\sigma}{2 \epsilon_{o}}$

where, $\sigma$ is the surface charge density

Following this, the formula for the electric force acting on a proton is given as:

F = eE

where, e is the charge of a proton

According to Newton's second law of motion, the overall force on the proton can be expressed as follows.

F = ma

a = $\frac{eE}{m}$

= $\frac{e(\frac{\sigma}{2 \epsilon_{o}})}{m}$

= $\frac{e \sigma}{2m \epsilon_{o}}$

According to kinematic equations, the proton's speed in the perpendicular direction can be described as follows.

$v_{f} = v_{i} + at$

= $(0 m/s) + \frac{e \sigma}{2 m \epsilon_{o}}t$

= $\frac{1.6 \times 10^{-19}C \times 2.34 \times 10^{-9} C/m^{2} \times 5.40 \times 10^{-8}s}{2 \times (1.67 \times 10^{-27} kg)(8.85 \times 10^{-12} C^{2}/Nm^{2}}$

= 683.974 m/s

Thus, the overall speed of the proton can be calculated as follows.

v' = $\sqrt{(960 m/s)^{2} + (683.974 m/s)^{2}}$

= $\sqrt{921600 + 467820.43}$

= $\sqrt{1389420.43}$

= 1178.73 m/s

Consequently, we conclude that the proton's speed is 1178.73 m/s.

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