Finding where Magnetic Fields = 0

[nmacholl]

Homework Statement

Two point charges, -520x10^-6C and -270x10^-6C are 2 meters apart. At which point would a carbon nucleus experience zero net force?
(positive test charge)

Homework Equations

k=9x10⁹
F=k((q₁*q₂)/r²) Coulomb's Law
E=k(q₁/r²)=(F/q₂)

The Attempt at a Solution

I really don't understand the method to solving the problem. A simply outline of what to find and then how to manipulate the equations to get the distance would really help me solve this. Fiddling has gotten me nowhere.

Thanks

 

[LowlyPion]

There are 2 forces acting on the test charge.

Where the forces are equal ...

If that point is X meters from one charge then it must be 2 - X from the other.

Just a little bit of algebra should give you what you need.

Btw: This has nothing to do with magnetism.

 

[thomate1]

for your question! I can provide you with a response to this problem.

First, it is important to understand that magnetic fields are created by moving charges. In this problem, we are dealing with two point charges that are stationary, so we are actually looking for the point where the electric field (not magnetic field) is equal to zero.

To find this point, we can use Coulomb's Law, which states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. In this case, we have two negative charges, so the force between them will be repulsive.

We can set up an equation using Coulomb's Law to find the distance at which the force between the two charges is equal to zero. This will give us the distance at which a positive test charge (such as a carbon nucleus) would experience zero net force.

F = k((q1*q2)/r^2)

Where:
F = force between the two charges
k = Coulomb's constant (9x10^9 N*m^2/C^2)
q1, q2 = the two charges (-520x10^-6 C and -270x10^-6 C)
r = distance between the two charges

Since we want to find the distance at which the force is equal to zero, we can set F = 0 and solve for r.

0 = k((-520x10^-6 C)*(-270x10^-6 C)/r^2)

0 = 9x10^9 * (140x10^-12 C^2)/r^2

r^2 = (9x10^9 * (140x10^-12 C^2))/0

r^2 = 0 (since anything multiplied by 0 is equal to 0)

Therefore, the distance at which the force between the two charges is equal to zero is 0 meters. This means that a positive test charge placed at this distance would experience zero net force.

I hope this explanation helps you understand the method for solving this problem. Let me know if you have any further questions. Good luck with your homework!