Electric Field of Nonconducting Solid Sphere

In summary, to calculate the magnitude of electric field at a point outside a charged sphere, the formula E=kq/r^2 should be used, where r is the distance from the center of the sphere to the point of interest.
  • #1
goteamusa
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Homework Statement



A nonconducting solid sphere of radius 2.30 cm carries a uniformly distributed positive charge of 8.00×10-9 C. Calculate the magnitude of electric field at 1.60 cm away from the center of sphere


Homework Equations



E=kqr/R^3



The Attempt at a Solution



(8.99x10^9)(8x10^-9)(.16)/(.23^2)=217.53 N/C

Clearly this solution is not correct, but I do not understand why using the formula did not work.
 
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  • #2
Can someone please explain where I went wrong?

The formula you used, E=kqr/R^3, is for the electric field at a point on the surface of a charged sphere. However, in this problem, the point of interest is 1.60 cm away from the center of the sphere, which is not on the surface.

To calculate the electric field at a point outside of a charged sphere, you need to use the formula E=kq/r^2, where r is the distance from the center of the sphere to the point of interest. In this case, r=1.60 cm.

So the correct calculation would be:

E=(8.99x10^9)(8x10^-9)/(1.60^2)= 1.77x10^5 N/C

Hope this helps!
 

What is the formula for the electric field of a nonconducting solid sphere?

The formula for the electric field of a nonconducting solid sphere is given by E = kQr / r^3, where E is the electric field, k is the Coulomb's constant, Q is the total charge of the sphere, and r is the distance from the center of the sphere to the point where the electric field is being calculated.

How does the electric field vary with distance from the center of the sphere?

The electric field of a nonconducting solid sphere decreases with distance from the center, following an inverse cube law. This means that as the distance increases, the electric field decreases at a faster rate.

What is the direction of the electric field at any point outside the sphere?

The direction of the electric field at any point outside the sphere is radial, meaning it points directly away from or towards the center of the sphere. This direction is determined by the sign of the total charge of the sphere.

Can the electric field inside a nonconducting solid sphere be non-zero?

No, the electric field inside a nonconducting solid sphere is always zero. This is because the charge on the surface of the sphere creates an equal and opposite electric field that cancels out the electric field inside the sphere.

How does the electric field of a nonconducting solid sphere compare to that of a conducting solid sphere?

The electric field of a nonconducting solid sphere follows an inverse cube law, while the electric field of a conducting solid sphere is constant throughout the space inside the sphere. This means that the electric field of a nonconducting solid sphere decreases faster with distance from the center compared to a conducting solid sphere.

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