Finding the charge density that produces a specific field

Neolightdraco · Mar 22, 2018

Homework Statement

Multiple-choice problem 7: electric field in spherical polar coordinates E = a sin(theta) r-hat + b cos(theta) theta-hat, with four options for charge density involving epsilon_0, 2a sin^2(theta) and b cos(2theta) over r sin(theta) or r.

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Using Gauss law,

Handwritten derivation on lined paper applying Gauss's law, q_enc/ε0 = ∮E·ds, with a surface integral of E sinθ, equated to a triple integral over r, θ and φ, leading to σ = 2ε0(2a sin²θ + b sin2θ)/sinθ.

Since there has been no mention of which type of charge density we have to find out I assumed it to be surface charge density since Gauss Law is in surface intergration , and I don't think there is any need to doing integration since the options given are results obtained without integration , I just can't get what's wrong

Is the problem in my choice of charge density or my method of solving it wrong?

Homework Equations

The Attempt at a Solution

kuruman · Mar 22, 2018

Have you tried Gauss's Law in differential form?

Neolightdraco · Mar 22, 2018

kuruman said:

Have you tried Gauss's Law in differential form?

No, I will try that

Finding the charge density that produces a specific field

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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