A cylindrical wire is carrying a current that is non-uniform in both space and t

Question

A cylindrical wire is carrying a current that is non-uniform in both space and time and can be described by the function s(r,t)=5(r2-3)t3.

a) 1. What units should the '5' in the above equation have in order for the units to work out in SI units?

b) 2. 2. Find an equation that describes magnetic field inside the wire due to the current as a function of r from the center of the wire.

c) 3.If all the numbers in the equation given have the appropriate SI units, how many Coulombs of charge go by a point in the wire after 3ms?  How many electrons does this represent?

Explanation / Answer

a) The over all unit for your equation should be Amperes

And opening s(r,t) = 5r2t3-15t3 will have units ampere

so 5r2t3 has units Ampere

So 5 has unit = Ampere/m2s3 = A.m-2.s-3

c) Since charge is also dependent on r therefore our answer is in form of r.

s(r,3*10^-3) = 5(r2-3)(27*10^-9) Coulombs / second

No of electrons = 5(r2-3)(27*10^-9) / 1.6*10^-19

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