Non-Uniform Distribution of Charge on a Rod

In summary, a rod of length L with a non-uniformly distributed charge Q=ax is placed on the x-axis with its left end at the origin. The constant a can be found to be a=(2Q)/(L^2). The potential due to this charged rod at a point on the positive x-axis, past the end of the rod, can be calculated by integrating (ax dx)/(4pi)(ε0)r, where r is the distance from the charge. In part c, a point charge +2Q is placed at 3L from the origin on the positive x-axis, and the potential energy of the system can be calculated using the equation dU=Vdq.
  • #1
mouzis
5
0

Homework Statement



A rod of length L lies along the x-axis with its left end at the origin. A total charge Q is distributed non-uniformly on the rod, so that ?=ax, where a is a positive constant. (a)Determine the constant a. (b) What is the potential due to this charged rod at a point along the positive x-axis, past the end of the rod? (c) A point charge +2Q is placed at 3L from the origin on the positive x-axis. What is the potential energy of this system?

Homework Equations


dq=λds
dV=(dq)/(4pi)(ε0)r
dU=Vdq

The Attempt at a Solution


I completed part a and got a=(2Q)/(l2)

my attempt at part b:
V=∫dV=∫(ax dx)/(4pi)(ε0)r

From there my question is more what is the value of r? is it x? From there I am sure i can figure out the rest.
 
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  • #2
r is the distance from the charge. A picture would help.

ehild
 

1. What is non-uniform distribution of charge on a rod?

Non-uniform distribution of charge on a rod refers to a situation where the electric charge is not evenly distributed along the length of the rod. This means that different parts of the rod have different amounts of charge.

2. How does non-uniform distribution of charge occur on a rod?

Non-uniform distribution of charge can occur on a rod when the charge is added or removed from specific areas of the rod, or when the rod is in contact with other charged objects. The charge can also be influenced by the shape, material, and size of the rod.

3. What are the effects of non-uniform distribution of charge on a rod?

Non-uniform distribution of charge can lead to an electric field around the rod, causing the rod to attract or repel other charged objects. It can also cause the rod to experience a net force and move in a particular direction.

4. How can non-uniform distribution of charge on a rod be measured?

The charge distribution on a rod can be measured using an electrometer or a charge detector. These devices can detect the presence of charge and measure the strength of the electric field around the rod.

5. How can non-uniform distribution of charge be controlled on a rod?

Non-uniform distribution of charge can be controlled by grounding the rod, which allows excess charge to flow to the ground and equalize the distribution. It can also be controlled by adjusting the shape or material of the rod to evenly distribute the charge.

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