Solving a 3-Charge Electrical Field Inside an Insulator Ball

[ori]

please help

given insulator ball with radius R that charged with uniformed density p<0.
the ball is charged with -3Q

3 colon charges with Q>0 each one, are found inside the ball (look at the draw)
the charges found at triangle that it's sides are equal (each side length = d)
and d<=2R
the triangle found at a plane that divide the ball to two equal areas.
given that all the system is balanced, found the length d between the charges

draw at http://s7.yousendit.com/d.aspx?id=269C621FA10036C8DC0AB7CAB624D86E


thanks!

 

[member 553083]

The length d between the charges can be found using Gauss' Law. If we consider the electric field at the surface of the ball, we have:E*A = (p*4*pi*R^2) where E is the electric field strength, A is the surface area of the ball, p is the charge density and R is the radius of the ball. Since the charges are located on a plane that divides the ball into two equal areas, the electric field strength at the plane will be half of the electric field strength at the surface of the ball. Therefore, we can calculate the electric field strength at the plane as:E(plane) = (p*2*pi*R^2) / 2 Now, we can use Coulomb's Law to calculate the force between the three charges:F = (Q^2 * 3) / (d^2) We can equate this force to the electric field strength at the plane in order to solve for d:(Q^2 * 3) / (d^2) = (p*2*pi*R^2) / 2 Therefore, we can solve for d as follows:d = (Q*sqrt(3*2*pi*R^2)) / sqrt(p)

 

[wais]

To solve this problem, we can use the concept of electric potential and Coulomb's law. First, we need to find the electric potential at the center of the ball, where the three charges are located. This can be done by using the formula V = kQ/r, where k is the Coulomb's constant, Q is the charge of each of the three charges, and r is the distance from the center of the ball to each of the charges.

Since the ball is charged with a uniform density, we can find the electric potential at the center of the ball by integrating the electric potential over the entire volume of the ball. This will give us the total electric potential at the center of the ball, which can be set equal to zero since the system is balanced.

Next, we can use the concept of electric field to find the electric field at the center of the ball. This can be done by taking the derivative of the electric potential with respect to distance. We can then set this electric field equal to zero, since the system is balanced.

Now, we can use Coulomb's law to find the distance d between the three charges. This can be done by setting the electric field equal to zero and solving for d. Since the triangle formed by the three charges is equilateral, we can use the Pythagorean theorem to find the length of each side of the triangle, which is equal to d.

In summary, to solve this problem we need to use the concepts of electric potential, electric field, and Coulomb's law. By setting the electric potential and electric field equal to zero, we can solve for the distance d between the three charges. This will give us the balanced system of three charges inside the insulator ball.