Question

A. The formula for B(I,z) assumes you're measuring B exactly in the center of the Coil along z. In other words, if you measured B ina different place, not along z, the formula would be invalid. Why? (B is a vector. Make a drawing. )  

(this is pertaining to Magnetic Fields)

B. Why didn't you just plot B vs. z? Explain.  

Answer 1

a . as we can see from the diagram

wben we take magentic field of the ring at ay other point other than the axis of the coil, the distance of the point from the individual elements of the coils is differnet, ranging from r1 to r2, and the direction of the magnetic field with horizontal axis is also varying, from alpha to beta

hence this means that the formula wehre we considered r and theta to be constant will be invalid

hence we cannot use the formula to calculate magnetic field on a point which is not at the axis of the coil

b. we plotted B as a function of z on axis only and not everywhere because then we would need to plot a 3d graph that will have varying values of magneitc field depending on x, y and the z coordinate of the pint, and this general experssino is more diffucit to compute as well as plot