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Course: Class 12 Physics (India) > Unit 1
Lesson 11: Application of Gauss lawElectric field due to spherical shell of charge
Electric field due to a charged spherical shell
Part 1- Electric field outside a charged spherical shell
Let's calculate the electric field at point , at a distance from the center of a spherical shell of radius , carrying a uniformly distributed charge .
Why is the electric field radial, outside the sphere?
[Task] - Come up with an argument to prove that the electric field must be radial & only depend on the distance from the center, .
STEP 1 - Choosing a Gaussian surface
Now that we know what the electric field looks like everywhere, choose a Gaussian surface that would make calculating the electric flux, easy.
Now that we have chosen a closed surface, we are ready to apply Gauss law & calculate the electric field.
STEP 2 - Simplifying the left-hand side (L.H.S.) of Gauss's law
STEP 3 - Simplifying the right-hand side (R.H.S.) of Gauss's law.
STEP 4 - Equating L.H.S & R.H.S
Now we can equate both sides of Gauss's law & calculate the electric field strength at point
Putting it all together
Part 2 - Electric field inside the charged spherical shell
STEP 2 - Simplifying the L.H.S. of Gauss's law
STEP 3 - Simplifying the R.H.S. of Gauss's law
STEP 4 - Equating L.H.S & R.H.S
Now we can equate both sides of Gauss's law & calculate the electric field strength inside the shell.
Let's summarise
Want to join the conversation?
- I understand everything except one thing...
Why is the electric field radial ?(9 votes)- to my understanding because the charge is unformly spread across the surface. and when we did the integration for the electric field of a uniformly charged surface. at any point the field was perpendicularto the surface.
if we take very small pieces of the surface they will be planar too and thus why we have radial electric field.
i kinda had the same doubt and this is the best ive been able to come up with,somebody correct me please if im wrong.(7 votes)
- But we learned that E at a point is = k q/r^2 r-hat. How do we now have a different definition for E?
Edit: just found that k = 1 / 4 pi epsilon. which is how it's written in the vids(4 votes)