1989 Physics B Electro - Question #2.

[GP_Skier]

Homework Statement

Two point charges, Q1 and Q2, are located a distance 0.20 meter apart, as shown above. Charge Q1 = +8.0*10^-6C. The net electric field is zero at point P, located 0.40 meter from Q1 and 0.20 meter from Q2. Charge Q2 = -2.0*10^-6C.

Determine the coordinate of the point R on the x-axis between the two charges at which the electric potential is zero.

Homework Equations

There is an x-axis in which Q1 is located at 0, Q2 is located at 0.2, and P is located at 0.4 (all in meters).

The Attempt at a Solution

I can't figure out what formula to use in order to find the location... what should I use?

 

[Shooting Star]

What is the potential at a point at a distance of x from a point charge q?

 

[Moetasim]

I would approach this problem by first identifying the relevant equations and principles that can be applied. In this case, we are dealing with electric charges and electric fields, so the relevant equations would be Coulomb's Law and the principle of superposition. Coulomb's Law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The principle of superposition states that the net electric field at a point is the vector sum of the individual electric fields created by each charge.

Using these principles, we can determine the electric field at point P by calculating the individual electric fields created by Q1 and Q2 and then adding them together. Since the net electric field at point P is zero, we can set this sum equal to zero and solve for the distance at which the electric potential is zero.

To do this, we can use the formula for the electric field created by a point charge, E = kQ/r^2, where k is the Coulomb's constant (8.99*10^9 Nm^2/C^2), Q is the charge, and r is the distance from the charge. We can then set up the following equation:

0 = kQ1/(0.4)^2 + kQ2/(0.2)^2

Solving for Q1, we get:

Q1 = -2Q2

Substituting this into the equation, we get:

0 = (-2Q2)(1/0.4^2 + 1/0.2^2)

Solving for Q2, we get:

Q2 = -4.5*10^-6 C

Now, using the formula for electric potential, V = kQ/r, we can find the coordinate of point R where the electric potential is zero. Setting V = 0 and solving for r, we get:

0 = kQ1/(0.4-r) + kQ2/r

Solving for r, we get:

r = 0.133 meters

Therefore, the coordinate of point R is 0.133 meters on the x-axis.