Eight solid plastic cubes, each 3.00 cm on each edge, are glued together to form

Question

Eight solid plastic cubes, each 3.00 cm on each edge, are glued together to form each one of the objects (i, ii, iii, and iv) shown in the figure below. (a) Assuming each object carries charge with uniform density of 400 nC/m^3 throughout its volume, find the charge of each object. (b) Assuming each object carries charge with uniform density 20.0 nC/m^2 everywhere on its exposed surface, find the charge on each object. (i) (ii) (Hi) (iv) (c) Assuming charge is placed only on the edges where perpendicular surfaces meet, with a uniform density 85.0 pC/m, find the charge of each object. (i) (ii) (Hi) (iv)

Explanation / Answer

For problem A, all you're really doing is adding up charges. Note that it gives the charge in nC/m3 - this means volume, three dimensional space. Note the units: square meters. Right now we don't know how many square meters each object is, but we do know that they are 3.00cm on each side. First, let's convert the volume of one of these cubes into square meters.

We need our units to be in meters first. 1cm = .01m, so 3cm = .03m

.03 x .03 x .03 = .000027m3

Now all we have to do is apply that 400nC/m3 value to the .000027m that we have

400 x .000027 = .0108nC

Every little cube in these objects has .0108nC of charge. Fortunately we know that each object is composed of eight cubes; therefore .0108 x 8 = .0864nC is the charge on each object.

Follow this model for the other questions; make sure that you convert the units you have, cm, into the units provided, meters. Then total up how many "units" you have - for example, in question 2, you just need to think three-dimensionally and count the total number of squares of exposed space. Then apply your units to the provided value, and that should be your answer.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.