Helmholtz coils are frequently used in experiments because they create a uniform magnetic field about their central axis. For example, they are traditionally used in the experiment for the measurement of the charge-to-mass ratio of the electron. Helmholtz coils are two coils separated by a distance equal to their radius and also carry equal currents in the same direction, as shown in the figure. Suppose the radius of the coils is R = 18.50 cm and each coil carries a current of I = 9.00 A and has N = 420.0 turns. The coils are in the yz plane where one coil's center is at x = 0 the other coil's center is at x = R. Using the Biot-Savart law, determine the expression for the resultant magnetic field B, along the line x joining their centers. Express the magnetic field in terms of the radius of the coils R, the number of turns N, the current I, x, and the permeability of free space, lo- B = 00 Ex= R Evaluate the magnetic field B, at x = 4.625 cm ( R) and x = 13.88 cm (GR). B, (4.625) = B. (13.88) = T

Helmholtz coils are frequently used in experiments because they create a uniform magnetic field about their central axis. For example, they are traditionally used in the experiment for the measurement of the charge-to-mass ratio of the electron. Helmholtz coils are two coils separated by a distance equal to their radius and also carry equal currents in the same direction, as shown in the figure. Suppose the radius of the coils is R = 18.50 cm and each coil carries a current of I = 9.00 A and has N = 420.0 turns. The coils are in the yz plane where one coil's center is at x = 0 the other coil's center is at x = R. Using the Biot-Savart law, determine the expression for the resultant magnetic field B, along the line x joining their centers. Express the magnetic field in terms of the radius of the coils R, the number of turns N, the current I, x, and the permeability of free space, lo- B = 00 Ex= R Evaluate the magnetic field B, at x = 4.625 cm ( R) and x = 13.88 cm (GR). B, (4.625) = B. (13.88) = T

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Helmholtz coils are frequently used in experiments because they create a uniform magnetic field about their central axis. For example, they are traditionally used in the experiment for the measurement of the charge-to-mass ratio of the electron. Helmholtz coils are two coils separated by a distance equal to their radius that carry equal currents in the same direction." Suppose the radius of the coils is R 18.00 cm and each coil carries a current of /== 11.50 A and has N 340.0 turns. The coils are in the yz plane where one coil's center is at x = 0 the other coil's center is at x = R. -X=R 00
A rod of mass 0.720 kg and radius 6.00 cm rests on two parallel rails (see figure below) that are d = 12.0 cm apart and L = 45.0 cm long. The rod carries a current of I = 36.0 A in the direction shown and rolls along the rails without slipping. A uniform magnetic field of magnitude 0.400 T is directed perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod as it leaves the rails? (Assume that the rod is of uniform density.) L 2.07 X You appear to have omitted the translational kinetic energy of the rod. m/s
A 1000 kg automobile drive west along the equator near Lake George in Uganda. At this location the earth’s magnetic field is 3.5 x 10 ^-5 T and points north parallel to the earth’s surface. If the automobile carries a charge of -20 x 10^-6 charge, how fast must it move so that the magnetic force balances 0.010 percent of its weight?
As shown in the figure, a small particle of charge q= 6.3 µ C and mass 3.84 x 1012 kg has velocity 9.0 x 10° m/s as it enters a region of uniform magnetic field. The particle is observed to travel in the semicircular path shown, with radius R= 5.0 cm. Calculate the magnitude and direction of the magnetic field in the region in T. If the field is into the page, give a negative number. If the field is out of the page, give a positive number. Region of magnetic field R Path of the particle
A 12.6 g wire of length 62.8 cm is suspended by a pair of flexible leads in a uniform magnetic field of magnitude 0.342 T (see the figure). What is the (a) magnitude and (b) direction (left or right) of the current required to remove the tension in the supporting leads? (a) Number (b) Units X L
As shown above, a positively charged particle moves to the right without deflection through a pair of charged plates. Between the plates are a uniform electric field E of magnitude 5.6 N/C and a uniform magnetic field B of magnitude 2.9 T, directed as shown in the figure. The speed of the particle is most nearly? v =________ m/s
An electron moves in a circle of radius r = 5.75 x 10-11 m with a speed 1.64 x 106 m/s. Treat the circular path as a current loop with a constant current equal to the ratio of the electron's charge magnitude to the period of the motion. If the circle lies in a uniform magnetic field of magnitude B = 6.96 mT, what is the maximum possible magnitude of the torque produced on the loop by the field? Number i Units
A five-sided object, whose dimensions are shown in the drawing, is placed in a uniform magnetic field. The magnetic field has a magnitude of 0.30 T and points along the positive y direction. Determine the magnetic flux through each of the five sides.