Another concentric sphere electric field question

Gold Member
[SOLVED] another concentric sphere electric field question

Interestingly, the very next question does specify uniformly distributed charges. This inconsistency has me worried that we were not to make that assumption in the 1st question from the other thread. Time to visit the office hours!

Homework Statement

Two concentric plastic spherical shells carry uniformly distributed charges, Q on the inner shell and –Q on the outer shell. Find the electric field (a) inside the smaller shell, (b) between the shells, and (c) outside the larger shell.

The Attempt at a Solution

I imagine the answer for (a) is no field, (b) is same as the previous question, only negative:$$\overrightarrow E = \frac{{ - Q}}{{4\pi r^2 \varepsilon _0 }}{\rm{\hat r}}$$

But I'm not sure about (c). I'm guessing it would be
$$\overrightarrow E = \frac{Q}{{4\pi r_1^2 \varepsilon _0 }}{\rm{\hat r }} - \frac{Q}{{4\pi r_2^2 \varepsilon _0 }}{\rm{\hat r}}$$
where r1 is the distance to the outer shell and r2 is the distance to the inner shell. Is this right? Is there a better way to express this or to simplify this expression?

Perhaps
$$\overrightarrow E = \frac{1}{{4\pi \varepsilon _0 }}\left( {\frac{Q}{{r_1^2 }}{\rm{\hat r }} - \frac{Q}{{r_2^2 }}} \right){\rm{\hat r}}$$

The Attempt at a Solution

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Shooting Star
Homework Helper
Ans to (a) is correct.

Why is there a minus sign is (b)? The charge on the inner shell is +Q...

In (c), you have goofed up badly. In the other thread, what did you mean by r? I'm leaving it to you to clear the mess up.

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