Potential along the X Axis due to Charge Distribution?

In summary, the conversation discusses the graph of potential along the x-axis for a uniformly charged square, with the textbook stating that it forms a bell-curved shape with a maximum at x=0. The question is then raised about why there is a maximum, despite the potential equation for a point charge suggesting it should approach positive infinity as x approaches zero. The response clarifies that the potential for a charged square is not the same as for a point charge, and that the potential at a point due to the four sides of the square can be found by using the expression for potential from a line charge multiplied by four. The conversation ends with the acknowledgment of the clear explanation provided.
  • #1
Joseph Nechleba
4
0
I have a question regarding electric potential and infinity. So,

"A square of side length a with uniformly distributed positive charge lies on the yz plane with its center at the origin. What does the graph of the potential along the x-axis look like?

The answer given in the textbook is a bell-curved-shaped graph with its maximum at x=0. My question is, Why is there a maximum? According to the equation for potential of a point charge, v = k|Q|/(x), shouldn't the potential approach positive infinity as x approaches zero from either direction, as electric potential is a scalar and the charge is uniform?

I am hoping someone can clear my conceptual misunderstanding.
 
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  • #2
Potential for a point charge is kq/x but the same expression is not true for a charged square. Take a point at a distance x from centre of square along x axis. Now find the potential at that point due to 4 sides of the square. You must know the expression for potential at a point due to a line charge. That times 4 will give total potential because potential is scalar.
 
  • #3
That makes perfect sense! Thank you for your prompt response!
 

1. What is potential along the X axis due to charge distribution?

Potential along the X axis due to charge distribution is a measure of the work needed to move a unit positive charge from a reference point to a specific point along the X axis in the presence of a charge distribution. It is also known as electric potential or voltage.

2. How is potential along the X axis calculated?

Potential along the X axis is calculated using the equation V(x) = kq/x, where k is the Coulomb's constant, q is the magnitude of the charge distribution, and x is the distance from the reference point to the specific point along the X axis.

3. What is the relationship between potential and distance along the X axis?

The potential along the X axis is inversely proportional to the distance from the reference point. This means that as the distance increases, the potential decreases and vice versa.

4. How does a change in charge distribution affect potential along the X axis?

A change in charge distribution will result in a change in potential along the X axis. An increase in charge distribution will lead to an increase in potential, while a decrease in charge distribution will result in a decrease in potential.

5. What are the SI units for potential along the X axis?

The SI unit for potential is volts (V), which is equivalent to joules per coulomb (J/C). This unit represents the amount of potential energy per unit charge at a specific point along the X axis.

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