How Do You Calculate Work Required to Move a Charge Near a Charged Cylinder?

AI Thread Summary
To calculate the work required to move a charge near a charged cylinder, one must first determine the electric field generated by the cylinder using its uniform charge density. The electric field can be found using Gauss's Law, which applies to cylindrical symmetry. Once the electric field is established, the work done in moving the charge can be calculated by integrating the force exerted on the charge over the distance moved. The user is seeking clarification on the final numerical answer, which should be in the form of 2.5X * 10^something. Assistance is needed to resolve the calculation accurately.
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I have a question that I am hoping someone can help me with, and I would like to say thank you to everyone who looks at this and tries to help.

We have a cylinder with uniform charge density of 2*10^-6 C/m^3, with a radius of 0.05m. How do I figure out how much work is required to move a charge of 4*10^-12C from 0.1m to 0.07m (distances from the center of the cylinder).

The answer should be 2.5X * 10^ something (don't know exactly), but I can't figure out how to do this. Someone please help.

Thanks
 
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can someone please help? i am very screwed if i don't figure this out. thanks.
 
nobody knows?
 
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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