# Electric field from spherically symmetric charge distributio

In summary, the electric field strength at 10cm is 2x103N/C, the electric flux through a 20cm diameter spherical surface that is concentric with the charge distribution is 251.3Nm2/C, and the charge inside the 20cm diameter spherical surface is 2.24x10^-9C.

## Homework Statement

A spherically symmetric charge distribution produces the electric field E=(200/r)r(hat)N/C, where r is in meters.
a) what is the electric field strength at 10cm?
b)what is the electric flux through a 20cm diameter spherical surface that is concentric with the charge distribution?
c)How much charge is inside this 20cm diameter spherical surface?

## Homework Equations

φe=∫E⋅dA=Qenclosed0

## The Attempt at a Solution

question a is pretty straightforward:
a) E=(200/.1m)N/C=2x103N/C
part b is where I get stuck, here's my attempt:
∫E⋅dA=Qenclosed0, Qenclosed is just some charge distribution so let's say we know it and keep it in its variable form, Qenclosed.
∫E⋅dA=Qenclosed0→EA=Qenclosed0
since the 20cm diameter spherical surface we drew is a known shape (spherical) we can use it as a gaussian surface?
E4πr2=Qenclosed0→E=KQenclosed/r2. Clearly I see the problem of having two unknowns here.

I guess the problem says nothing about what the dimensions of the "spherical symmetric charge distribution" is... maybe this comes into play?

The problem states what the electric field goes as
so for part b:
E=(200/.1m)N/C, our r for part b is the radius of the 20cm concentric spherical surface is 10cm→.1m
E=2000N/C
Φe=EA=2000N/C(4π0.1m2)=251.3Nm2/C

If this is correct then part c should be easy:
φe=∫E⋅dA=EA=Qenclosed0
we just solved for fluxφe
φeε0=Qenclosed therefore,
Qenclosed=(251.3Nm2/C)(8.85x10^-12C2/Nm2)=2.24x10^-9C

Is there a hint buried somewhere in the problem that should tell me that the electric field should go as E=σ/2ε0, σ being charge/area?
If so where?
if not should I assume the electric field goes as E=KQ/r2?

## 1. What is a spherically symmetric charge distribution?

A spherically symmetric charge distribution refers to a situation where a charge is uniformly distributed around a spherical object, such as a sphere or a point charge.

## 2. How is the electric field calculated from a spherically symmetric charge distribution?

The electric field from a spherically symmetric charge distribution is calculated using Coulomb's Law, which states that the magnitude of the electric field at a point is directly proportional to the amount of charge and inversely proportional to the square of the distance from the charge.

## 3. Is the electric field the same at all points around a spherically symmetric charge distribution?

Yes, the electric field from a spherically symmetric charge distribution is the same at all points that are equidistant from the center of the distribution. This is because the electric field is radial, meaning it points directly away from or towards the center of the distribution.

## 4. How does the electric field change as the distance from the charge distribution increases?

The electric field from a spherically symmetric charge distribution decreases as the distance from the charge increases. This is because the electric field is inversely proportional to the square of the distance from the charge.

## 5. Can a spherically symmetric charge distribution have a net electric field of zero?

Yes, a spherically symmetric charge distribution can have a net electric field of zero if the amount of positive charge is equal to the amount of negative charge. In this case, the electric field vectors from each charge cancel each other out, resulting in a net electric field of zero.

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