Question

An infinite, nonconducting sheet has a surface charge density σ = +5.21 pC/m2. (a) How much work is done by the electric field due to the sheet if a particle of charge q0 = 3.20 × 10-19 C is moved from the sheet to a point P at distance d = 2.44 cm from the sheet? (b) If the electric potential V is defined to be zero on the sheet, what is V at P?

Answer 1

a) W = 2.26 × 10⁻²¹ J

b) V = - 0.00706 Volts

Step-by-step explanation:

Given:

The surface charge density, σ = +5.21 pC/m²

Charge of the particle, q₀ = 3.20 × 10⁻¹⁹

distance, d = 2.44 cm = 0.024 m

Now, the electric field (E) due to the uniformly charged sheet is given as:

`E = (\sigma)/(2\epsilon_o)`

a) The work done is given as:

W = q₀Ed

substituting the values, we get

W =
`3.20* 10^(-19)(5.21* 10^(-12))/(2* 8.85* 10^(-12))* 0.024`

W = 2.26 × 10⁻²¹ J

b) The electric potential (V) at point P is given as:

V = - Ed

substituting the values, we get

V = - (
`(5.21* 10^(-12))/(2* 8.85* 10^(-12))* 0.024`)

V = - 0.00706 Volts