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

[torquey123]

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

 

[robb_]

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.

 

[m2003]

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.