(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two spherical conductors are connected by a long conducting wire, and a charge of 10.2 Micro-coulombs is placed in the combination. One sphere has a radius of 5.99 cm and the other has a radius of 7.99cm. What is the electric field near the surface of the smaller sphere. Answer in units of V/m.

2. Relevant equations

V = kQ/r

E = kQ/r^{2}

k=8.99 x 10^{9}

q_{1}+ q_{2}= Q

r_{1}/r_{2}= q_{1}/q_{2}

3. The attempt at a solution

My only issue with this problem is trying to find the individual charges on both spheres. I know that they obviously need to add up to 10.2 micro-coulombs and that the ratio of the charges should be equal to the ratio of the radii. What I've been doing is trying to find the charges using the formula for voltage for both spheres and setting them equal to each other since they are connected by the same wire. Using the net charge formula, I set q_{2}to be equal to 10.2e-6 - q_{1}. Now after I substitute that into the voltage formula, I get:

kq_{1}/.0799 = (k(10.2e-6 q_{1}))/.0599

After isolating q_{1}I get,

q_{1}= 6.802838063e-6

After subtracting that from the total charge, I get the other charge to be 3.397161937e-6

Even though they add up to be 10.2e-6, I come down to the problem that the ratio does not equal that of the radii which is 1.333889816.

I've been at this for the past 2 hours trying to find mistakes in my math and I can't seem to find out what I am doing wrong. Any help is appreciated.

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# Homework Help: Spherical conductors connected by a wire.

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