How Does Electric Potential Change with Distance from a Charged Sheet?

[adp5025]

Heres the problem:
An infinite nonconducting sheet has a surface charge density of 5.80 pC/m^2. How much work is done by the electric field due to the sheet if a particle of charge q = 1.60x10^-19 C is moved from the sheet to a point P at distance d = 3.56 cm from the sheet? Also if the electric potential V is defined to be zero on the sheet what is V at P.

Ok so here's what i tried doing:

using the equations E = density / 2(8.85E-12) to find E
using E i tried finding Volts using the equation V = EdsCos
after that i used V to solve for Work using the equation
V = -w/q

got nothing close to the answer

as reference the answers in the back of the book say
a) 1.87E-21 J
b)-11.7mV

I don't know what I am doing please help

 

[Nate810]

.Solution:To find the electric field due to the sheet, use the equation E = ρ/2ε₀, where ρ = 5.80 pC/m², ε₀ = 8.85x10^-12 C²/(Nm²). This gives E = 2.58x10^6 N/C. To find the work done by the electric field, use the equation W = qV, where q = 1.60x10^-19 C. The potential at P is V = E•d•cosθ, where d = 3.56 cm and θ = 0° since the charge is being moved perpendicular to the sheet (the electric field due to the sheet is normal to the sheet). This gives a potential of V = -11.7 mV. Finally, the work done is W = qV = 1.87x10^-21 J.

 

[kyle8921]

I would recommend reviewing the equations and units used in your calculations. It is important to make sure that all units are consistent and that the equations used are appropriate for the given situation. In this case, the equation V = EdsCos may not be the correct one to use, as it assumes a uniform electric field, which may not be the case for an infinite nonconducting sheet. Additionally, make sure you are using the correct value for the electric constant, which is 8.85 x 10^-12 C^2/Nm^2.

To solve for the work done by the electric field, you can use the equation W = qEd, where q is the charge of the particle, E is the electric field, and d is the distance moved. In this case, the electric field can be calculated using the equation E = σ/2ε0, where σ is the surface charge density and ε0 is the electric constant. Once you have calculated the electric field, you can plug in the values for q and d to solve for the work done.

To find the electric potential at point P, you can use the equation V = kq/r, where k is the Coulomb's constant, q is the charge of the sheet, and r is the distance from the sheet to point P. In this case, the electric potential at the sheet is defined as zero, so you can set V at the sheet to be 0. Then, solve for V at point P using the calculated value for the electric field.

It is also important to note that the electric potential is a scalar quantity, so it cannot have a direction like the electric field does. Therefore, the answer for part b should be -11.7 mV, not -11.7 mV/m. I hope this helps and good luck with your calculations!