How Do You Calculate Charge and Distance from Electric Potential and Field?

[nfcfox]

Homework Statement

The electric potential a distance r from a point charge q is 195 V, and the magnitude of the electric field is 2870 N/C. Find the values of q and r.

Homework Equations

2780q=F
Fr=W
W/q=195

The Attempt at a Solution

Using substitution I got r=.00679 meters, which is correct. I can't substitute to find q... I have no idea what to do.

 

[gneill]

What are the equations for the electric field and electric potential at a distance r from a point charge q? Your text or class notes must have these two equations as they are quite fundamental. Hint: They both involve the constant from Coulomb's law.

 

[nfcfox]

What are the equations for the electric field and electric potential at a distance r from a point charge q? Your text or class notes must have these two equations as they are quite fundamental. Hint: They both involve the constant from Coulomb's law.

Ik the equation F=(kQ1Q2)/(r^2) that's Coulomb's law. We never really did anything with fields or potentials... I found that electric field=F/q which I already have up there.

What are the equations for the electric field and electric potential at a distance r from a point charge q? Your text or class notes must have these two equations as they are quite fundamental. Hint: They both involve the constant from Coulomb's law.

I already have the electric field equation up there and the electric potential is U=(kQq)/r

 

[gneill]

Ik the equation F=(kQ1Q2)/(r^2) that's Coulomb's law. We never really did anything with fields or potentials... I found that electric field=F/q which I already have up there.

I already have the electric field equation up there and the electric potential is U=(kQq)/r

I suspect that your method for finding the distance r was actually flawed, and your correct result was a coincidence. I say this because one of your relevant equations, Fr = W, is not correct for this situation. If F is meant to be force and W the work done, then it doesn't hold if the force varies with the distance (F is not constant so W = F⋅d doesn't hold).

Your new equation, U=(kQq)/r, gives the electric potential energy (in Joules) for a system of two charges. That's the energy required to bring them from infinity to a separation distance of r. What you need is the electric potential (in Volts) for a point charge at distance r.

The equations that you're seeking are:

$E = k \frac{q}{r^2}~~~~~~~~~~$ Electric field strength (N/C)

$V = k \frac{q}{r}~~~~~~~~~~~$ Electric potential (Volts)

You should verify that these equations are given in your textbook.