Electric potential at point x on the axis of a ring of charge density eta

In summary, to find the electric potential at point x on the axis of a ring of charge density \eta = cr, you can integrate the charge density over the disk to compute the total charge, Q, and then use this to eliminate c in the equation for electric potential. The final expression should include R and Q, but not c.
  • #1
Bng1290
5
0
Electric potential at point x on the axis of a ring of charge density "eta"

Homework Statement


A circular disk of radius R and total charge Q has the charge distributed with surface charge density [tex]\eta[/tex] = cr, where c is a constant. Find an expression for the electric potential at distance z on the axis of the disk. Your expression should include R and Q, but not c.

Homework Equations



[tex]\eta[/tex]=cr where c is constant
V=(1/4pi[tex]\epsilon[/tex])(Q/r)
V=[tex]\Sigma[/tex]Vi

The Attempt at a Solution


So what I did was to sum all Vi and i was able to pull (1/4pi[tex]\epsilon[/tex]) and (1/sqrt(z^2+R^2) out which leaves me with Q left in the sum which I know i need to relate to [tex]\eta[/tex] in some way. The problem I'm having here is that I just don't understand how to work with [tex]\eta[/tex]=cr in such a way as to get rid of the constant c in my answer.

I feel like I'm not grasping this problem as a whole so any help would be wonderful. Thanks!
 
Physics news on Phys.org
  • #2


To eliminate c, since \eta = cr, you can integrate the charge density over the disk to compute the total charge, Q. This should give you c in terms of Q and R.
 
  • #3


Nice! Thanks so much!
 

FAQ: Electric potential at point x on the axis of a ring of charge density eta

1. What is the formula for calculating electric potential at point x on the axis of a ring of charge density eta?

The formula for calculating electric potential at point x on the axis of a ring of charge density eta is V = k*Q*x/(x^2 + R^2)^(3/2), where k is the Coulomb constant, Q is the total charge of the ring, x is the distance from the center of the ring to the point, and R is the radius of the ring.

2. How does the electric potential at point x change as the distance from the ring changes?

The electric potential at point x on the axis of a ring of charge density eta decreases as the distance from the ring increases. This is because the electric potential is inversely proportional to the distance from the source of the electric field, which in this case is the ring.

3. Can the electric potential at point x ever be negative?

Yes, the electric potential at point x can be negative. This occurs when the point is located within the ring, at a distance less than the radius. In this case, the electric potential is negative because the electric field is in the opposite direction of the direction of the point's movement.

4. How does the charge density eta affect the electric potential at point x?

The charge density eta has a direct effect on the electric potential at point x. As the charge density increases, the electric potential also increases. This is because a higher charge density means a greater amount of charge is present in the ring, resulting in a stronger electric field and higher electric potential at point x.

5. Is the electric potential at point x affected by the size of the ring?

Yes, the size of the ring, specifically the radius, does affect the electric potential at point x. As the radius increases, the electric potential at point x decreases. This is because a larger radius means a greater distance between the point and the ring, resulting in a weaker electric field and lower electric potential at point x.

Similar threads

Finding electric potential of an infinite line charge at z axis
2
Replies
64
Views
3K
Potential and Electric Field near a Charged CD Disk
Replies
2
Views
967
What is taken as datum level for the following absolute potentials?
Replies
2
Views
316
Calculating Electric Potential for a Non-Negligible Thickness Toroid
Replies
4
Views
1K
Why is electric field at the center of a charged disk not zero?
Replies
4
Views
2K
Calculating Linear Charge Density of a Cylinder
Replies
1
Views
2K
Uniform charge density and electric potential
Replies
4
Views
3K
Charge on a grounded conducting sphere in a uniform electric field, after ungrounding and movement
Replies
1
Views
741
How Is the Electric Field Calculated for a Point Outside a Charged Ring?
Replies
11
Views
2K
Find the electric field between 2 finite discs
Replies
16
Views
520

Hot Threads

Recent Insights

Back
Top