Question

For the expression you derived in question 1, show that the maximum/minimum value of the function you obtained is at the midpoint between the two coils. Is the midpoint between the two coils a maximum or a minimum? Show your calculation/derivation on a separate piece of paper. 2. 3. Make a plot of the magnetic field at the midpoint between the two coils as a function of . Does your plot confirm your conclusion in question 2? Explain your answer

the result from part one is in pen

i just need help with parts 2 and 3

thanks!

Answer 1

Fig: Two coils separated by a distance R equal to the radius of the coils A/c to the Biot-savart law the magnetic field due to single wire loop is (at point P) B = mu_0 IR^2/2 [R^2 + x^2]^3/2 1 I = coil current (Amp) R = coil radius (m) but here x = R/2 and if coils consists of N turns of wire than equation 1 become B = mu_0 NIR^2/2 [R^2 + R^2/4]^3/2 B = mu_0 NI R^2/2 times (5/4)^3/2 middot R = mu_0 NIR/2/B 5 squareroot 5 = 4 mu_0 NIR/5 squareroot 5 2 from symmetry, the magnetic field strength at the midpoint P will be twice of the single coil value B_net = 2B 3 equation 2 using in 2 we get B_net = 2 times 4 u_) N I R/5 squareroot 5 = 8 mu_0 N I R/ squareroot 125 B_net = 8 mu_0 N I R