Find the magnitude of the magnetic field inside the solenoid when it carries a c

Question

Find the magnitude of the magnetic field inside the solenoid when it carries a current of 0. 610 A. Calculate the number of turns per unit length. Substitute n and I into Equation 19. 16 to find the magnitude of the magnetic field. Find the momentum of a proton orbiting in a circle of radius 0. 034 m near the center of the solenoid. Write Newton's second law for the proton. Substitute for centripetal acceleration a = v2 / r. Cancel one factor of v on both sides and multiply by r, getting momentum mv. Approximately how much wire would be needed to build this solenoid? Multiply the number of turns by the circumference of one loop. n = N / l = 111 turns / 0. 128 m = 0. 87 times 103 turns / m B = mu0nI B = (4pi times 10-7 T. m / A)(8. 67 times 102 turns / m)(0. 610 A) B = 6. 64 times 10-4 T ma = F = qvB mv2 / r = qvB mv = rqB = (0. 034 m)(1. 60 times 10-19 C)(6. 64 times 10-4 T) p = mv = kg. m / s length of wire (number of turns)(2pir) = (1. 11 times 102 turns)(2pi. 0. 0511 m) length of wire = m An electron in part (b) would have the same momentum as the proton, but a much higher speed. It would also orbit in the opposite direction. The length of wire in part (c) is only an estimate, because the wire has a certain thickness, slightly increasing the size of each loop. In addition the wire loops aren't perfect circles, because they wind slowly up along the solenoid. Suppose you have a 34. 3 m length of copper wire. If the wire is wrapped into a solenoid 0. 240 m long and having a radius of 0. 0554 m, how strong is the resulting magnetic field in its center when the current is 13. 8 A? B = T

Explanation / Answer

b)p = mv = 3.61216 * 10-24 kgm/sec

c)l = 35.64m

19.8) B = NI/l

N = 34.3/(2**0.0554) = 98.5381687 Turns

n = N/l = 410.5757

B = 0.00712 T

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