Finding the radius of a charged metal sphere

[Jimmy25]

Homework Statement

A metal sphere centered at the origin has a surface charge density that has a magnitude of 24.6 nC/m2 and a radius less than 2.00 m. At a distance of 2.00 m from the origin, the electric potential is 540 V and the electric field strength is 270 V/m. (Assume the potential is zero very far from the sphere.)

1. What is the radius of the sphere?
2. Is the charge on the sphere positive or negative?

Homework Equations

The Attempt at a Solution

I found the radius as 0.623 m but how do I determine the sign of the charge on the sphere?

 

[payumooli]

shouldn't the electric field tell you the charge of the particle creating it

 

[kerimek]

To determine the sign of the charge on the sphere, you can use the formula for electric potential at a distance from a charged sphere:

V = kQ/r

where V is the electric potential, k is the Coulomb's constant, Q is the charge on the sphere, and r is the distance from the center of the sphere.

Since the potential is positive (540 V), the charge on the sphere must also be positive. This is because the electric potential is directly proportional to the charge, so an increase in potential means an increase in charge.