Coulombs Law Problem: Find Point Along Y-Axis for Zero Electric Field

In summary, there are two charges, -4.1 microC at the origin and -2.98 microC at 2.11519 m along the y-axis. The Coulomb constant is 8.99x10^0. The question asks for the point on the y-axis where the electric field is zero, and the equations used are E= F/q and F=kQq/r^2. The attempt at a solution involves setting the two electric fields equal to each other and solving for x, but the answer obtained was incorrect. The person seeking help is advised to first intuit where the field will be zero before attempting to solve the problem.
  • #1
torquey123
4
0

Homework Statement



A charge of -4.1 microC is located at the origin and a charge of -2.98microC is located along the y-axis at 2.11519 m.
The value of the Coulomb constant is 8.99x10^0.
At what point along the y-axis is the electric field zero? Answer in units of meters.



Homework Equations



E= F/q

F=kQq/r^2

The Attempt at a Solution



kq/x^2 = Q/(2.11519-x)^2

using this, and doing the math i got 1886 something...very incorrect.. Please help:confused:
 
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  • #2
1. Both charges produce an electric field.
2. What will happen to a test charge placed at a position where the electric field is zero?
3. You should first intuit where the field will be zero. I.E. is it along the negative y axis, between the charges, or past the second charge along the y axis.
Hope that helps.
 
  • #3



I would approach this problem by first understanding the concept of Coulomb's Law and its equation, which states that the magnitude of the electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This can be mathematically represented by the equation F = kQq/r^2, where k is the Coulomb constant, Q and q are the charges, and r is the distance between them.

In this problem, we are given two charges, -4.1 microC and -2.98 microC, located at the origin and 2.11519 m along the y-axis, respectively. We are asked to find the point along the y-axis where the electric field is zero, which means that the net force between the two charges is also zero.

To find this point, we can use the equation E = F/q, where E represents the electric field, F is the net force between the two charges, and q is the test charge. Since we want the electric field to be zero, we can set E = 0 and solve for q.

Substituting the given values into the equation, we get:

0 = k(4.1x10^-6)(2.98x10^-6)/r^2

Solving for r, we get:

r = √(k(4.1x10^-6)(2.98x10^-6)/0)

Using the given value for the Coulomb constant, we get:

r = √(8.99x10^9(4.1x10^-6)(2.98x10^-6)/0)

Simplifying, we get:

r = √(1.2118)

r = 1.1 m

Therefore, the point along the y-axis where the electric field is zero is located at 1.1 m from the origin.
 

1. What is Coulomb's Law?

Coulomb's Law is a fundamental law of physics that describes the electrostatic interaction between charged particles. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

2. How do you calculate the electric field using Coulomb's Law?

The electric field can be calculated by dividing the force between two charges by the magnitude of one of the charges. The resulting value is the electric field strength at that point in space.

3. What is the significance of finding a point along the y-axis with zero electric field?

Finding a point along the y-axis with zero electric field is important because it allows us to identify the location where the electric field is cancelled out due to the presence of two equal and opposite charges. This point is known as the electric field zero or null point.

4. Can Coulomb's Law be applied to systems with more than two charges?

Yes, Coulomb's Law can be applied to systems with any number of charges. However, the calculation becomes more complex as the number of charges increases, and other methods such as vector addition may be necessary to determine the total electric field at a given point.

5. How does distance affect the strength of the electric field according to Coulomb's Law?

According to Coulomb's Law, the strength of the electric field decreases as the distance between two charges increases. This is because the force between two charges is inversely proportional to the square of the distance between them, meaning that the farther apart the charges are, the weaker the electric field will be at a given point.

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