Force Acting on Charge on Metal Ball: Irodov Problem 3.69

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In summary, The problem involves finding the modulus of the vector of the resultant force on a charge located on one half of a metal ball with radius 1.5 cm and charge 10e-6 C. The solution involves using Gauss's law to find E, then integrating E_z over the hemisphere.
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-marko-
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A metal ball or radius R=1.5[cm] has a charge q=10e-6[C]. Find the modulus of the vector of the resultant force acting on a charge located on one half of the ball.

I found a solution on http://irodov.nm.ru/3/resh/3_69.gif but I don't understand explanations regardind to the problem so I would appreciate if anyone could explain a solution.
 
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You need to show your work before you get help.

Which part of the solution are you stuck in?
 
  • #3
The whole problem is a little bit fuzzy to me (E', Eokp, E and relations between them), so it would be very helpful if you could explain main steps in solving this problem (without doing integration, just basic steps and formulae).

Thanks.
 
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-marko- said:
A metal ball or radius R=1.5[cm] has a charge q=10e-6[C]. Find the modulus of the vector of the resultant force acting on a charge located on one half of the ball.
1. Find E using Gauss's law.
2. E_z=Ecos\theta=Qrcos\theta/R^3.
3. Integrate E_z\rho over the hemisphere.
 
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What is the formula for calculating the force acting on a charge on a metal ball?

The formula for calculating the force acting on a charge on a metal ball is F = qE, where F is the force in newtons, q is the charge in coulombs, and E is the electric field in newtons per coulomb.

How do you determine the direction of the force acting on a charge on a metal ball?

The direction of the force acting on a charge on a metal ball can be determined by the direction of the electric field. If the electric field points towards the ball, the force will be in the same direction. If the electric field points away from the ball, the force will be in the opposite direction.

What is the difference between the force acting on a charge on a metal ball in an electric field and a gravitational field?

The force acting on a charge on a metal ball in an electric field is directly proportional to the strength of the electric field and the magnitude of the charge, while the force of gravity on an object is only determined by the mass of the object and the strength of the gravitational field. Additionally, the force of gravity always points towards the center of the object, while the direction of the electric force can vary depending on the direction of the electric field.

How does the distance between the charge and the metal ball affect the force acting on the charge?

The force acting on the charge on a metal ball is inversely proportional to the square of the distance between the two objects. This means that as the distance increases, the force decreases. This is known as the inverse square law.

How do you solve for the magnitude of the electric field given the force acting on a charge and the magnitude of the charge?

To solve for the magnitude of the electric field, divide the force acting on the charge by the magnitude of the charge. This will give you the electric field in newtons per coulomb.

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