Force on a part of a spherical shell on the other

AI Thread Summary
To calculate the electrostatic force on one part of a charged conducting sphere due to the other part after a plane cuts it, the initial approach involves dividing the sphere into infinitely thin discs and integrating the forces between them. This method can become complex and cumbersome. An alternative suggested is to use the Maxwell stress tensor, which may simplify the calculations. The participant expresses unfamiliarity with the Maxwell stress tensor but is open to exploring it for a more efficient solution. Understanding the Maxwell stress tensor could provide a clearer framework for solving the problem.
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Homework Statement


Given there is a conducting sphere which has a charge q on it. A plane cuts the sphere into 2 form a distance r from centre. How can we calculate the electrostatic force on one part on either side of the plane due ro the other part?

Homework Equations

The Attempt at a Solution


I tried to divide one part and divided it into infinitely thin disc. Then i calculated the force due to this disc on the other part of sphere. This was done again by deviding the other part into small parts and then finding force due to the infinitesimal disc on the other infinitesimal didc and then integrate it. Ghis process looks very messy. Is there any other way yo solve it?
 
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Are you familiar with the Maxwell stress tensor?
 
Orodruin said:
Are you familiar with the Maxwell stress tensor?
Nope. But thanks for the reply. I will refer to it and try it out.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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