Kelvin
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Find the net force that the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere. Express your answer in terms of the radius R and the total charge Q
[the "model" answer is \frac{1}{4 \pi \epsilon_0} \frac{3 Q^2}{16 R^2}]
my attempt:
regard two hemispheres as two point charges located at their center of mass, \frac{3 R}{8} from the center.
so
<br /> <br /> F = \frac{1}<br /> {{4\pi \varepsilon _0 }}\frac{{\left( {Q/2} \right)^2 }}<br /> {{\left( {2 \times \frac{3}<br /> {8}R} \right)^2 }} = \frac{1}<br /> {{4\pi \varepsilon _0 }}\frac{4}<br /> {9}\frac{{Q^2 }}<br /> {{R^2 }}<br /> <br />
but I got it wrong...
so, can anyone tell me how should I start?
[the "model" answer is \frac{1}{4 \pi \epsilon_0} \frac{3 Q^2}{16 R^2}]
my attempt:
regard two hemispheres as two point charges located at their center of mass, \frac{3 R}{8} from the center.
so
<br /> <br /> F = \frac{1}<br /> {{4\pi \varepsilon _0 }}\frac{{\left( {Q/2} \right)^2 }}<br /> {{\left( {2 \times \frac{3}<br /> {8}R} \right)^2 }} = \frac{1}<br /> {{4\pi \varepsilon _0 }}\frac{4}<br /> {9}\frac{{Q^2 }}<br /> {{R^2 }}<br /> <br />
but I got it wrong...
so, can anyone tell me how should I start?