Where Should a 30nC Charge Be Placed to Nullify Electric Field at the Origin?

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In summary, the problem involves finding the location of a point charge that will result in a zero electric field at the origin. The given information includes the positions and magnitudes of two charges, as well as the formula for electric field intensity. After setting E=0 and solving for the position of the third charge, the solution is found to be at (0, 2.07, -4.14). The key step is dividing y by z in the equation.
  • #1
LeeroyJenkins
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Homework Statement


In free space, Q1 = 10nc at P1(0,-4,0) and Q2 = 20nC at P2(0,0,4).
a. Find E at the origin (answered)
E(r) = 5.617ay - 11.235az
b. Where should a 30nC point charge be located so E=0 at the origin? (need help)

Homework Equations


E(r) = (1/4(pi)epsilon) sum ((Qm)am/(|r-rm|^2))
formula for electric field intensity

The Attempt at a Solution


E = 0, Q3 = 30nC
E = 0 = (1/4(pi)epsilon) ( (Q1)a1/(|r-r1|^2))+ ...)
a3 = (0-x)ax + (0-y)ay + (0-z)az/ |r-r3|
x = 0
P3 = (0, y, z)

5.617ay - 11.235 az = ((Q3)a3/(|r-r3|^2))

*5.617ay - 11.235 az = Q3((0-y)ay + (0-z)az/ |r-r3|^3)
**|r-r3| = sqrt(0^2 + (0-y)^2 + (0-z)^2)
* and ** aren't enough to solve I'm missing one thing any help would be appreciated.
 
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  • #2
(0, -5.62, +11.23) = (3x10-8+12)/(4pi8.854) (0, -y, z)\(y 2+z 2) 1.5 ; -5.62 = 270 -y/(y 2+z 2) 1.5 and 11.23 = 270 -z/ (y 2 + z 2); -0.5 = y/z, (y 2 + 4y 2)1.5=48y, y=2.07, z = -4.14, The location is (0, 2.07, -4.14). The trick is dividing y by z!
 
  • #3


To find the position of Q3 where E=0 at the origin, we can set up the equation as follows:

E = 0 = (1/4(pi)epsilon) ( (Q1)a1/(|r-r1|^2))+ ...) + ((Q2)a2/(|r-r2|^2)) + ((Q3)a3/(|r-r3|^2))

Since we know the values of Q1, Q2, and E(r) at the origin, we can plug these in and solve for the position of Q3:

0 = (1/4(pi)epsilon) ( (10nC)(-4ay)/(|r-(0,-4,0)|^2))+ ...) + ((20nC)(4az)/(|r-(0,0,4)|^2)) + ((Q3)a3/(|r-r3|^2))

Simplifying, we get:

0 = (-40ay)/(16) + (80az)/(16) + ((Q3)a3)/(|r-r3|^2)

0 = (-2.5ay) + (5az) + ((Q3)a3)/(|r-r3|^2)

Since we want E=0 at the origin, we can set the coefficients of ay and az to 0, and solve for the position of Q3:

0 = (Q3)a3/(|r-r3|^2)

0 = (30nC)a3/(|r-r3|^2)

Solving for |r-r3|, we get:

|r-r3| = (30nC)/(a3)

Since a3 is a unit vector, we can assume that it has a magnitude of 1. Therefore, |r-r3| = 30nC.

This means that the distance between Q3 and the origin should be 30nC. We can also see from the equation that the position of Q3 should be in the direction of a3 (0, y, z), where y and z can take any value as long as the magnitude of |r-r3| is 30nC.

Therefore, the position of Q3 can be any point on a circle with a radius of 30nC centered at the origin.
 

Related to Where Should a 30nC Charge Be Placed to Nullify Electric Field at the Origin?

What does "Find Q3 Position for E=0" mean?

"Find Q3 Position for E=0" refers to finding the third quartile position for a set of data with a mean or expected value of 0. This is often done to analyze the distribution and spread of the data.

How is Q3 Position for E=0 calculated?

The Q3 Position for E=0 is calculated by first arranging the data in ascending order and then finding the median, which is the middle value. The third quartile position is then the value that is three-quarters of the way through the data set, or the median of the upper half of the data.

Why is Q3 Position for E=0 important in scientific research?

Q3 Position for E=0 is important in scientific research because it helps to understand the distribution and variability of data. By knowing the third quartile position, scientists can better analyze the data and make conclusions about the population being studied.

What does a high Q3 Position for E=0 indicate?

A high Q3 Position for E=0 indicates that the upper half of the data is skewed towards higher values. This could mean that there are outliers in the data or that the data is not normally distributed.

Can Q3 Position for E=0 be negative?

Yes, Q3 Position for E=0 can be negative if the data set includes negative values. The position itself does not have a specific range, as it is based on the data set being analyzed.

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