Graphing e field for ring charge

In summary, the equation E=(kqz)/(z^2+a^2)^1.5 has a maximum at z=a/sqrt(2) and a minimum at z=-a/sqrt(2). The book also confirms this answer. The graph of E versus z can be sketched by considering the values of E at z=0, the sign of E at negative values of z, the location of E=0, and the limits at infinity and -infinity.
  • #1
pyroknife
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Homework Statement


E=(kqz)/(z^2+a^2)^1.5 Through calculus i found that the max occurs at z=a/sqrt(2) and z=-a/sqrt(2) and I think the negative one is the minimum. That answer was given in the book also. The ring has radius a. It wants me to graph E versus z. I'm a little confused on how to graph this. the only 2 points I have on there are 1 max and 1 min but I don't know how to draw the general shape.

Homework Equations


The Attempt at a Solution

 
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  • #2
There are two points you know: the places of maximum and minimum. What is E at z=0? What is the sign of E at negative values of z? Where is E=0? What are the limits at infinity and at -infinity? From these, you can sketch the curve.

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Related to Graphing e field for ring charge

1. What is the purpose of graphing the electric field for a ring charge?

The purpose of graphing the electric field for a ring charge is to visually represent the strength and direction of the electric field at different points around the ring charge. This can help us understand the behavior of the electric field and make predictions about how a charged particle would move in its presence.

2. How is the electric field strength represented on the graph?

The electric field strength is typically represented by the length and direction of arrows on the graph. The longer the arrow, the stronger the electric field at that point. The direction of the arrow indicates the direction of the electric field.

3. What factors affect the strength of the electric field for a ring charge?

The strength of the electric field for a ring charge is affected by the magnitude of the charge, the distance from the charge, and the geometry of the ring. As the charge or distance from the charge increases, the electric field strength decreases. The shape and orientation of the ring can also affect the electric field strength.

4. How does the direction of the electric field change as we move around the ring charge?

The direction of the electric field changes as we move around the ring charge because the electric field is a vector quantity. This means that it has both magnitude and direction. The direction of the electric field at a point is always tangent to the electric field line passing through that point.

5. Can the electric field for a ring charge ever be zero?

Yes, the electric field for a ring charge can be zero at certain points, such as at the center of the ring or at points along the axis of the ring. This occurs because the electric field vectors from each point on the ring cancel out at these locations, resulting in a net electric field of zero.

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