Question

4. The expression for the magnetic field everywhere on the axis of a current loop which is located A Helmholr coil is comprised of two identical coils NIR at xo is B(x)- separated by the distance R, with each coil located at a distance xo +R/2 away from the origin (R is the radius of the coils), and where the current runs counterclockwise in both when viewed from the <+x-axis back towards the origin. A Helmholtz coi is a useful tool because the magnetic field at the center of the apparatus is large and nearly uniform. (a) Calculate the malgnetic field strength BH everywhere on the x-axis (expressed in terms of x), (b) then evaluate Bi(0) at the midpoint of the Helmholtz coil (i.e. atx -0). (c) Next, calculate the first derivative of the field (dB(x)/dr) and (d) evaluate it at the midpoint of the coils (dBldrlo),回If, on the other hand, you reverse the current in the left coil so that it is clockwise compared to the right one, you end up with a Maxwell coil. What is the magnetic field BA0 a the midpoint of the pair for a Maxwell coil, and ( what is the first derivative of the magnetic field evaluated at the midpoint (dB/dxo)? (g) Note any differences in the B field and its derivative between the Helmholtz and Maxwell configurations. (h) The quantity dB/dx is useful because it determines the force that is exerted on a magnetic moment (think "button magnet"), given by the relationship F (dBldr). Assuming values of N-500, R-15 cm. 1-3A, and μ-0.4 A-m2, calculate the strength of the B field and the actual force F on a button magnet at the midpoint of the coils in both the Helmholtz and )the Maxwell configuration. NOTES: Please express your final Before evaluating the expression for B at x-0, calculate all derivatives of B algebraically in terms of x. And finally, all calculations for the Maxwell coil are the same as those of the Helmholtz coil except for one sign difference, so you do not need to do the differentiation a second time Also, do not confuse the magnetic moment of the button magnet μ with the permeability of answers to parts b, d, e, and f in terms of free space ue.)

Answer 1

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