Simple Nature - Light and Matter

and the forces on them were measured:q 1 = 1 C , v 1 = 0 , F 1 = (1 N)ŷq 2 = 1 C , v 2 = (1 m/s)ˆx , F 2 = (1 N)ŷq 3 = 1 C , v 3 = (1 m/s)ẑ , F 3 = 0Determine the electric and magnetic fields.17 If you put four times more current through a solenoid, how√many times more energy is stored in its magnetic field?18 A Helmholtz coil is defined as a pair of identical circularcoils lying in parallel planes and separated by a distance, h, equalto their radius, b. (Each coil may have more than one turn of wire.)Current circulates in the same direction in each coil, so the fieldstend to reinforce each other in the interior region. This configurationhas the advantage of being fairly open, so that other apparatus canbe easily placed inside and subjected to the field while remainingvisible from the outside. The choice of h = b results in the mostuniform possible field near the center. A photograph of a Helmholtzcoil was shown in figure o on page 656.(a) Find the percentage drop in the field at the center of one coil,compared to the full strength at the center of the whole apparatus.√√Problem 18.(b) What value of h (not equal to b) would make this percentage√difference equal to zero?19 The figure shows a nested pair of circular wire loops usedto create magnetic fields. (The twisting of the leads is a practicaltrick for reducing the magnetic fields they contribute, so the fieldsare very nearly what we would expect for an ideal circular currentloop.) The coordinate system below is to make it easier to discussdirections in space. One loop is in the y − z plane, the other in thex − y plane. Each of the loops has a radius of 1.0 cm, and carries1.0 A in the direction indicated by the arrow.(a) Calculate the magnetic field that would be produced by one such√loop, at its center.(b) Describe the direction of the magnetic field that would be produced,at its center, by the loop in the x − y plane alone.(c) Do the same for the other loop.(d) Calculate the magnitude of the magnetic field produced by thetwo loops in combination, at their common center. Describe its√direction.Problem 19.Problem 20.Problems 721