Aconducting sphere of radius r carries positive charge q. calculate the amount of work that would be required to move a small positive test charge q0 slowly from r=5r to r=3r. assume that the presence of q0 has no effect on how the charge q is distributed over the sphere.

express your answer in terms of the electric constant ϵ0 and some or all of the variables q, q0, and r.

w=

Acarpenter builds an exterior house wall with a layer of wood 2.9 cm thick on the outside and a layer of styrofoam insulation 2.3 cm thick on the inside wall surface. the wood has k=0.080w/(m⋅k), and the styrofoam has k= 0.010 w/(m⋅k). the interior surface temperature is 19.0 ∘c , and the exterior surface temperature is -15.0 ∘c . a.)what is the temperature at the plane where the wood meets the styrofoam? celsius b.)what is the rate of heat flow per square meter through this wall? /m^2