Finding r using point charges and work done by an electric force

In summary, a positive point charge of +8.9 x 10^-8 C is located at an equipotential surface A with a radius of 1.3 m. A positive test charge of +2.7 x 10^-11 C moves from surface A to another equipotential surface B with an unknown radius rB. The work done by the electric force as the test charge moves from surface A to surface B is -8.3 x 10^-9 J. To find rB, we can use the equation V = kq/r, where k is the Coulomb's constant, q is the charge, and r is the distance. By rearranging the equation, we get r = kq/V
  • #1
Rae_4
4
0

Homework Statement


A positive point charge (q = +8.9 10-8 C) is surrounded by an equipotential surface A, which has a radius of rA = 1.3 m. A positive test charge (q0 = +2.7 10-11 C) moves from surface A to another equipotential surface B, which has a radius rB. The work done by the electric force as the test charge moves from surface A to surface B is WAB = -8.3 10-9 J. Find rB.


Homework Equations


VB=VA-(WAB/q0)
V=kq/r



The Attempt at a Solution


kq/rB=kq/rA-(WAB/q0)


I don't seem to understand the concepts behind this question and cannot come up with the correct answer. I'm really lost. Any help explaining this would be appreciated.
 
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  • #2
Do you know what electric potential is?
Do you know how potential relates to potential energy and to work?
Do you know what an equi-potential surface is?

Consider: what would be the equation for the work needed to lift an object mass m from height y1 to height y2 close to the surface of the Earth?
How about if y1 and y2 were not close to the Earth?
 
  • #3
Welcome to PF!

Hi Rae_4! Welcome to PF! :smile:
Rae_4 said:
A positive point charge (q = +8.9 10-8 C) is surrounded by an equipotential surface A, which has a radius of rA = 1.3 m. A positive test charge (q0 = +2.7 10-11 C) moves from surface A to another equipotential surface B, which has a radius rB. The work done by the electric force as the test charge moves from surface A to surface B is WAB = -8.3 10-9 J. Find rB.

The surfaces are imaginary.

It just means that the test charge moves from distance 1.3 to distance rB, but not necessarily in a straight radial line. :wink:

Show us what you've tried. :smile:
 

What is "r" in the context of point charges and work done by an electric force?

"r" refers to the distance between two point charges or the distance between a point charge and a specific point in space where the electric force is being measured.

How is "r" calculated?

"r" is calculated using the distance formula, which is the square root of the sum of the squares of the differences in the x, y, and z coordinates between the two points.

How do point charges affect the value of "r"?

The value of "r" is directly affected by the magnitude and sign of the point charges. If the charges are of the same sign, the distance between them will decrease, resulting in a smaller value for "r". If the charges are of opposite signs, the distance between them will increase, resulting in a larger value for "r".

What is the relationship between "r" and the work done by an electric force?

There is an inverse square relationship between "r" and the work done by an electric force. This means that as the distance between the two charges increases, the work done by the electric force decreases, and vice versa.

Can "r" be negative?

No, "r" cannot be negative as it represents a distance, which is always a positive value. However, the direction of "r" can be negative, indicating the direction of the force between the two charges.

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