Finding the mass of a sphere with uniform charge density

In summary, the problem involves a sphere with radius R and uniform volume charge density P that is placed above an infinite sheet of paper with uniform surface charge density u. The sphere remains stationary and the task is to find its mass. The equation for the volume of a sphere is 4/3 pi R^3 and the equation for force is F=ma. The key is to find the forces acting on the ball to solve for its mass.
  • #1
ghost34
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Homework Statement


The sphere has radius R, and uniform volume charge density P. This sphere remains stationary (levitates) when placed above an infinite sheet of paper with a uniform surface charge density u. What is this sphere's mass?

Homework Equations


4/3 pi R^3 is the volume of a sphere
F=ma

The Attempt at a Solution


The only connection between mass and the charged situation I can see is with the Force=ma law, but as there isn't any acceleration, I can't figure out how to solve for m...any help would be appreciated, thanks
 
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  • #2
To remain stationary, the net force on the ball should be zero. What are the forces acting on the ball?
 

FAQ: Finding the mass of a sphere with uniform charge density

What is the equation for finding the mass of a sphere with uniform charge density?

The equation for finding the mass of a sphere with uniform charge density is m = (4/3)πρr³, where m is the mass, ρ is the charge density, and r is the radius of the sphere.

How do I determine the charge density of a sphere?

The charge density of a sphere can be determined by dividing the total charge of the sphere by its volume. The formula is ρ = Q/V, where ρ is the charge density, Q is the total charge, and V is the volume of the sphere.

Can I use this equation for spheres with non-uniform charge density?

No, this equation is only applicable for spheres with uniform charge density. For spheres with non-uniform charge density, the equation for mass will vary depending on the distribution of the charge.

What is the unit of mass used in this equation?

The unit of mass used in this equation is typically kilograms (kg). However, you can use any unit of mass as long as it is consistent with the units used for charge density and radius.

Can this equation be applied to objects other than spheres?

Yes, this equation can be applied to any three-dimensional object with a uniform charge density. However, the shape of the object will determine the formula for calculating its volume. For example, the volume of a cube is calculated by V = s³, where s is the length of one side of the cube.

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