Question

An infinite nonconducting sheet has a surface charge density σ = 8.00 pC/m².

(a) How much work is done by the electric field due to the sheet if a particle of charge q = +1.60 ✕ 10⁻¹⁹ C is moved from the sheet to a point P at distance d = 3.52 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) Work done by the electric field due to the sheet which is given as :

using an equation,   E = / 2 ₀                                                                { eq.1 }

where, = surface charge density = 8 x 10^-12 C/m²

₀ = constant value = 8.85 x 10^-12 C²/Nm²

inserting the values in above eq.

E = (8 x 10^-12 C/m²) / 2 (8.85 x 10^-12 C²/Nm²)

E = (8 x 10^-12 C/m²) / (17.7 x 10^-12 C²/Nm²)

E = 0.451 N/C

And   electric force is given by, F = q E                                               { eq.2 }

where, q = charge on particle = +1.6 x 10^-19 C

inserting the values in eq.2,

F = (+1.6 x 10^-19 C) (0.451 N/C)

F = 0.721 x 10^-19 N

finally, using an equation W = F d                                                      { eq.3 }

where, d = distance between particle and sheet = 3.52 cm = 0.0352 m

inserting the values in eq.3,

W = (0.721 x 10^-19 N) (0.0352 m)

W = 0.0253 x 10^-19 J

W = 2.53 x 10^-21 J

(b) If the electric potential V is defined to be zero on the sheet, then the potential at point P will be given as :

using an equation,    V = - W / q                                                            { eq.4 }

inserting the values in eq.4,

V = - (2.53 x 10^-21 J) / ((+1.6 x 10^-19 C)

V = -1.58 x 10^-2 V