Repulsion Forces Between Northern & Southern Hemisphere of Metal Sphere

In summary, the force of repulsion between the "northern" hemisphere and the "southern" hemisphere of a metallic sphere with total charge Q is not zero due to the individual charge distributions and the electric field they create. While the net field inside the sphere is zero, the radially outward field outside the sphere causes the charges to spread out evenly on the surface and creates a net field that resembles a point charge at the center of the sphere. This is what keeps the charges confined to the outer surface and allows for mutual repulsion between the hemispheres.
  • #1
Lea
3
0

Homework Statement


A metal sphere of radius R carries a total charge Q. What is the force
of repulsion between the "northern" hemisphere and the "southern" hemisphere?

Homework Equations

The Attempt at a Solution


Since the sphere is metallic, its conducting and so the electric field inside the sphere is 0, and outside the sphere it is perpendicular to the surface and is radially outwards, and so, the force exerted by the northern hemisphere on the southern hemisphere should be 0. However, the answer appears to be other than zero. why?
 
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  • #2
The net field inside is zero because the all the individual fields from the individual charges distributed around the sphere cancel each other out in the interior. That does not say that those same fields don't serve to push all the charges to the skin of the sphere, keeping them spread out evenly over the surface.

As far as the mutual repulsion of hemispheres goes, you've still got two charge distributions pushing on each other.
 
  • #3
But those charge distributions have an electric field that is radially outwards, how can they push on each other?
 
  • #4
Lea said:
But those charge distributions have an electric field that is radially outwards, how can they push on each other?
Each charge has a spherically symmetric field radiating outward around itself. Exterior to the sphere the net effect of summing all the fields leaves just the radially outward part. Within the sphere they all cancel. The overall effect is to be able to perceive no field in the interior of the sphere and a radially outward field exterior to the sphere.

At the surface where the charges reside, they are feeling the effects of the net radial field. This is what keeps those charges confined to the outer surface. The fields aren't mutually canceled from there outward, so each of the individual charges is "feeling" a net field that looks as if all the charge Q were placed as a point charge at the center of the sphere (and the conducting sphere is ignored).
 
  • #5
Thank you! I understand now.
 

FAQ: Repulsion Forces Between Northern & Southern Hemisphere of Metal Sphere

What causes repulsion forces between the northern and southern hemisphere of a metal sphere?

The repulsion forces between the northern and southern hemisphere of a metal sphere are caused by the interaction between the magnetic fields of the two hemispheres. Each hemisphere has its own magnetic field, and when these fields interact, they create a repulsive force.

Why do repulsion forces occur specifically between the northern and southern hemisphere?

This is because the magnetic fields of the two hemispheres are oriented in opposite directions. Like poles of a magnet repel each other, and the same principle applies to the magnetic fields of the northern and southern hemisphere of a metal sphere.

Do all metal spheres experience repulsion forces between their hemispheres?

No, repulsion forces between the northern and southern hemisphere of a metal sphere only occur if the sphere is made of a magnetic material, such as iron or nickel. Non-magnetic metal spheres will not experience these forces.

Can the strength of the repulsion forces be controlled?

Yes, the strength of the repulsion forces between the northern and southern hemisphere of a metal sphere can be controlled by changing the strength of the magnetic fields. This can be done by using stronger or weaker magnets or by adjusting the distance between the two hemispheres.

What are some potential real-world applications of studying repulsion forces between the northern and southern hemisphere of a metal sphere?

Studying repulsion forces between the northern and southern hemisphere of a metal sphere can have various applications in industries such as manufacturing, transportation, and energy production. Understanding these forces can help improve the design and efficiency of magnetic levitation systems, electric motors, and generators. It can also aid in the development of new technologies, such as magnetic bearings and magnetic sensors.

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