Jackson 3.7 Three point charges (q,−2q,q) are located in ....

In summary, the conversation discusses a problem involving three point charges in a straight line and a grounded conducting spherical shell. The person has found a solution but is unsure why certain terms vanish in the solution. They specifically ask about the terms ##-\frac{1}{r}## and ##\frac{1}{b}-\frac{1}{r}## and their behavior at different values of l.
  • #1
Pual Black
92
1

Homework Statement


Hi,
The question is
"
Three point charges (q,−2q,q) are located in a straight line with separation a and with the middle charge (−2q) at the origin of a grounded conducting spherical shell of radius b ..."

I have found a solution for this problem but there is one step that I don't understand. I have uploaded the pdf file.
Last page the term ##-\frac{1}{r}## vanishes and at the bottom of the page the
##\frac{1}{b}-\frac{1}{r}## vanishes too. Can you tell me why?
 

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  • #2
at l=0 the term vanishes.
But what about the other values of l
 
Last edited:

Related to Jackson 3.7 Three point charges (q,−2q,q) are located in ....

1. How do I calculate the electric field at a point in space due to these three charges?

The electric field at a point in space is given by the equation E = kq/r^2, where k is the Coulomb constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the charge and the point in space. To find the total electric field at a point, simply calculate the electric field from each charge individually and then add them together vectorially.

2. What is the direction of the electric field at a point between two of the charges?

The direction of the electric field at a point between two charges is determined by the direction of the force that a positive test charge would experience if placed at that point. If the two charges are of equal magnitude, the electric field between them will be zero.

3. Can the electric field be negative at any point due to these charges?

Yes, the electric field can be negative at a point if the direction of the electric field due to one or more of the charges is opposite to the direction of the electric field due to the other charges. This can happen if the charges have different signs or if they are not equally spaced from the point in question.

4. How does the distance between the charges affect the electric field at a point?

The electric field at a point is inversely proportional to the square of the distance between the charges. This means that as the distance between the charges increases, the electric field at a point will decrease. Conversely, as the distance decreases, the electric field will increase.

5. What is the significance of the electric field in this scenario?

The electric field represents the force per unit charge that would be experienced by a test charge at a point in space. It is an important concept in understanding the behavior of electrically charged particles and how they interact with each other. In this scenario, the electric field helps to determine the direction and strength of the force that would be exerted on a charged particle placed at a point in space due to the presence of the three charges.

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