Question

A proton moves a distance 10 cm in a uniform electric field of 3.5 kN C, in the direction of the field.
Calculate the change in potential energy of the proton.

Answer 1

The change in potential energy of the proton is  5.6 x $10^{-17}$ Joule

What is a Uniform Electric Field ?

A uniform electric field is where the electric field strength is the same at all points in the field. In the uniform field, the force experienced by a charge is the same no matter where it is placed in the field.

Given that a proton moves a distance 10 cm in a uniform electric field of 3.5 kN C, in the direction of the field.

• The distance d = 10 cm = 0.1 m

• Electric field E = 3.5 KN/C

• Proton charge q = 1.6 x $10^{-19}$ C

The Work done = Fd

but F = Eq

Recall that Electric field E = F/q = V/d

Where V = potential difference.

Let us first calculate the V

E = V/d

V = Ed

Substitute all the parameters into the formula above

V = 3.5 × 10³ × 0.1

V = 350 v

from F/q = V/d

make F the subject of formula and substitute it in work formula

F = Vq/d

W.D = Vq/d x d

W.D = Vq

Substitute all the parameters into the formula above

W.D = 350 x 1.6 x $10^{-19}$

W.D = 5.6 x $10^{-17}$ J

Work done = Energy = Potential Energy

Therefore, the change in potential energy of the proton is 5.6 x $10^{-17}$ Joule

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