- #1
Kelvin
- 52
- 0
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 [tex]\frac{1}{4 \pi \epsilon_0} \frac{3 Q^2}{16 R^2}[/tex]]
my attempt:
regard two hemispheres as two point charges located at their center of mass, [tex]\frac{3 R}{8}[/tex] from the center.
so
[tex]
F = \frac{1}
{{4\pi \varepsilon _0 }}\frac{{\left( {Q/2} \right)^2 }}
{{\left( {2 \times \frac{3}
{8}R} \right)^2 }} = \frac{1}
{{4\pi \varepsilon _0 }}\frac{4}
{9}\frac{{Q^2 }}
{{R^2 }}
[/tex]
but I got it wrong...
so, can anyone tell me how should I start?
[the "model" answer is [tex]\frac{1}{4 \pi \epsilon_0} \frac{3 Q^2}{16 R^2}[/tex]]
my attempt:
regard two hemispheres as two point charges located at their center of mass, [tex]\frac{3 R}{8}[/tex] from the center.
so
[tex]
F = \frac{1}
{{4\pi \varepsilon _0 }}\frac{{\left( {Q/2} \right)^2 }}
{{\left( {2 \times \frac{3}
{8}R} \right)^2 }} = \frac{1}
{{4\pi \varepsilon _0 }}\frac{4}
{9}\frac{{Q^2 }}
{{R^2 }}
[/tex]
but I got it wrong...
so, can anyone tell me how should I start?