E-field inside a non-conducting hollow pear.

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To find the electric field inside a hollow non-conducting pear with a varying surface charge density, the discussion emphasizes the use of symmetry and Gauss's law. The charge density is zero at the top and 600 C/m^2 at the bottom, leading to the conclusion that the electric field inside the pear can be determined by superposition of fields in the x, y, and z directions. It is noted that due to the lack of enclosed charge within the hollow region, the electric field is zero overall, although the z-component may be non-zero. The approach suggests that applying Laplace's equation could be beneficial, but the primary conclusion rests on Gauss's law. Understanding the implications of the charge distribution is crucial for accurately determining the electric field.
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Homework Statement



Find the electric field inside a hollow non-conducting pear with a surface charge-distribution (axially symmetric too) of σ(r,θ). The charge density σ is zero at the top of the pear, and 600 C/m^2 at the bottom.

Homework Equations



I'm not sure how to approach the problem ... maybe some application of Laplace's equation.

The Attempt at a Solution



The electric field at any point inside the pear will be the superposition of x,y, and z fields. I assume that we can use symmetry about the z-axis to our advantage.
 
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Nevermind, it's just a simple application of gauss' law on the inside of the object yielding E=0 because there is no enclosed charge. (And E-z is non-zero I believe.)
 

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