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annms
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Not much more to add to the title. I was just wondering, under what conditions can a charged sphere be treated as a point charge?
When the charge distribution is spherically symmetric, the field outside the sphere is exactly that of a point charge at the center of the sphere. (Where the charge of the point charge equals the total charge of the sphere.)annms said:I was just wondering, under what conditions can a charged sphere be treated as a point charge?
chrisbaird said:"When can a charged sphere be treated as a point charge? "
This is only true if the sphere is isolated from everything else. If another charge, or another object held at some potential, is brought near the sphere, it will induce surface charges in the sphere that are not spherically symmetric, and therefore you can no longer treat it as a point charge. But if the radius of the sphere is very small compared to characteristic lengths of the system, then you can treat it as a point charge even if it is not isolated because the induced charges will be spherically symmetric as an approximation if the sphere is very small.
ZealScience said:But it can still be viewed as an point charge by taking a new gaussian surface where the centre shifts to the new equivalent point charge and take a larger sphere. Everywhere outside the surface the model is still valid.
But when there is an external charge the field is again distorted. Actually the net field should be modeled by another equivalent charge and a even larger sphere as gaussian surface.
ZealScience said:But it can still be viewed as an point charge by taking a new gaussian surface where the centre shifts to the new equivalent point charge and take a larger sphere. Everywhere outside the surface the model is still valid.
But when there is an external charge the field is again distorted. Actually the net field should be modeled by another equivalent charge and a even larger sphere as gaussian surface.
A charged sphere is a physical object with a net electric charge, meaning it has more positive or negative charges than the opposite charge. This can occur naturally or through the addition or removal of electrons.
To treat a charged sphere as a point charge means to simplify the physical object into a single point with all of its charge concentrated at that point. This is a simplification used in certain calculations and models.
A charged sphere can be treated as a point charge when the distance from the point of interest to the surface of the sphere is much larger than the radius of the sphere. This is known as the "far-field" approximation and is used to simplify calculations.
Treating a charged sphere as a point charge is a simplification and may not accurately represent the behavior of the actual physical object. This approximation is most accurate for objects with a uniform charge distribution and when the distance from the point of interest is significantly larger than the size of the sphere.
Treating a charged sphere as a point charge simplifies electric field calculations by reducing the complexity of the system. However, this simplification may lead to less accurate results, particularly for objects with non-uniform charge distributions or when the distance from the point of interest is not significantly larger than the size of the sphere.