Finding the potential difference?

[tyhwang1987]

Hi anyone can solve this problem?

A volume charge density of pv= 1/r^2 uC/m^3 exists in the region bounded by
1.0m < r < 1.5m. Find the potential difference between the point A(3.0, 4.0, 12.0) and
the point B (2.0, 2.0, 2.0).

Anyone can show me the solution for this problem?

 

[kbaumen]

To get help you should show your own work, show that you actually tried to solve it instead of coming here and asking others to do it.

And this should probably go in the homework section.

 

[Moetasim]

Sure, I'd be happy to help you solve this problem! To find the potential difference between points A and B, we first need to calculate the electric potential at each point. This can be done using the equation V = k*q/r, where V is the electric potential, k is the Coulomb's constant (9x10^9 Nm^2/C^2), q is the charge, and r is the distance between the point and the charge.

For point A, we can calculate the potential using the given volume charge density and the distance from the origin (r = √(3^2 + 4^2 + 12^2) = 13). Therefore, V(A) = (1/4πε0) * (1/r^2) * (4/3)π(1.5^3 - 1^3) = 0.0073 V.

Similarly, for point B, we can calculate the potential using the given volume charge density and the distance from the origin (r = √(2^2 + 2^2 + 2^2) = 3√3). Therefore, V(B) = (1/4πε0) * (1/r^2) * (4/3)π(1.5^3 - 1^3) = 0.0219 V.

Now, to find the potential difference between these two points, we simply subtract V(A) from V(B). Therefore, the potential difference between points A and B is V(B) - V(A) = 0.0219 V - 0.0073 V = 0.0146 V.

I hope this helps! Let me know if you have any other questions.