How Can I Solve This Electric Field Integral?

AI Thread Summary
The discussion centers on solving a challenging integral related to calculating the electric field above a spherical shell. The integral in question is ∫[(z-Ru)/(z^2+R^2-2zRu)^(3/2)] du, with limits from -1 to 1, where z and R are constants. Participants suggest that the integral can be found in standard physics textbooks or solved using online tools like Wolfram Alpha. The conversation emphasizes persistence in problem-solving and utilizing available resources for assistance. Overall, the integral's complexity is acknowledged, but solutions are deemed accessible through various methods.
PhysicsGirl90
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Hey guys,

While trying to calculate the electric field above a spherical shell i ran into this integral that i am having some difficulty solving.

∫[(z-Ru)/(z^2+R^2-2zRu)^(3/2)] du

-1 < u < 1

(z and R are known constants)

Can anyone help point me in the right direction? Thx
 
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PhysicsGirl90 said:
Hey guys,

While trying to calculate the electric field above a spherical shell i ran into this integral that i am having some difficulty solving.

∫[(z-Ru)/(z^2+R^2-2zRu)^(3/2)] du

-1 < u < 1

(z and R are known constants)

Can anyone help point me in the right direction? Thx

its easy ...keep trying or if u still dnt gt it dis integration is solved in any std physics book...
 
and if you can't get it , you can solve it by wolfram http://www.wolframalpha.com/input/?i=integral+%28a-b*x%29%2F%28a^2%2Bb^2+-+2*a*b*x%29^%283%2F2%29+dx
 
Do a google search for "the integrator wolfram"
 
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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