#3 Magnetic field strength in the center of a ring Suppose a conductor in the shapeof a perfectly circular ring bears a current of 0.451 Amperes. If the conductor has a radius of0.0100 meters, what is the magnitude of the magnetic field at the center of the ring? Recallthat 1 Gauss = 10-“ T, and that the magnetic field strength at the center of a single circularcurrent bearing ring is:HoiB =2rA. 0.283 GaussB. 0.417 GaussC. 0.612 GaussD. 0.845 Gauss

The expression for the magnetic field strength is, B=μ0i2r

Answered: #3 Magnetic field strength in the…

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter29: Sources Of The Magnetic Field

Section: Chapter Questions

Problem 10P

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The magnetic field at all points within the cylindrical region whose cross-section is indicated in the accompanying figure starts at 1.0 T and decreases uniformly to zero in 20 s. What is the electric field (both magnitude and direction) as a function of r, the distance from the geometric center of the region?
A long, vertical, metallic wire carries downward electric current. (i) What is the direction of the magnetic field it creates at a point 2 cm horizontally east of the center of the wire? (a) north (b) south (c) east (d) west (e) up (ii) What would be the direction of the field if the current consisted of positive charges moving downward instead of electrons moving upward? Choose from the same possibilities as in part (i).
Explain why the magnetic field would not be unique (that is, not have a single value) at a point in space where magnetic field lines might cross. (Consider the direction of the field at such a point.)
A particle in the cyclotron shown in Figure 28.16a gains energy qV from the alternating power supply each time it passes from one dee to the other. The time interval for each full orbit is T=2=2mqB so the particles average rate of increase in energy is 2qVT=q2BVm Notice that this power input is constant in time. On the other hand, the rate of increase in the radius r of its path is not constant. (a) Show that the rate of increase in the radius r of the panicles path is given by drdt=1rVB (b) Describe how the path of the particles in Figure 28.16a is consistent with the result of part (a). (c) At what rate is the radial position of the protons in a cyclotron increasing immediately before the protons leave the cyclotron? Assume the cyclotron has an outer radius of 0.350 m, an accelerating voltage of V = 600 V, and a magnetic field of magnitude 0.800 T. (d) By how much does the radius of the protons path increase during their last full revolution? Figure 28.16 (a) A cyclotron consists of an ion source at P, two does D1 and D2 across which an alternating potential difference is applied, and a uniform magnetic field. (The south pole of the magnet is not shown.) (b) The first cyclotron, invented by E. O. Lawrence and M. S. Livingston in 1934.
A particle with electric charge is fired into a region of space where the electric field is zero. It moves in a straight line. Can you conclude that the magnetic field in that region is zero? (a) Yes, you can. (b) No; the field might be perpendicular to the particles velocity. (c) No; the field might be parallel to the particles velocity. (d) No; the particle might need to have charge of the opposite sign to have a force exerted on it. (e) No; an observation of an object with electric charge gives no information about a magnetic field.
Noting that the magnetic field lines of a bar magnet resemble the electric field lines of a pair of equal and opposite charges, do you expect the magnetic field to rapidly decrease in strength with distance from the magnet? Is this consistent with your experience with magnets?
A cosmic ray electron moves at 7.50106m/s perpendicular to the Earth's magnetic field at an altitude where field strength is 1.00105T. What is the radius of the circular pain the electron follows?
A particle’s path is bent when it passes through a region of non-zero magnetic field although its speed remains unchanged. This is very useful for “beam steering’’ in particle accelerators. Consider a proton of speed 4106m/s entering a region of uniform magnetic field 0.2 T over a 5-cm-wide region. Magnetic field is perpendicular to the velocity of the particle. By how much angle will the path of the proton be bent? (Hint: the particle comes out tangent to a circle.
A mass spectrometer is being used to separate common oxygen- 16 from the much rarer oxygen-18, taken from a sample of old glacial ice. (The relative abundance of these oxygen isotopes is related to climatic temperature at the time the ice s deposited.) The ratio of the masses of these two ions is 16 to 18, the mass of oxygen-16 is 2.661026kg, , and they are singly charged and travel at 5.00106m/s in a 1.20-T magnetic field. What is the separation between their path when they hit a target after travet5ing a semicircle?
(a) Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a 0.500C charge and ?ies due west at a speed of 660 m/s ever the Earth’s south magnetic pole, where the 8.00105T magnetic field points straight up. What are the direction and the magnitude of the magnetic force on the plane? (b) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect.
A very large parallel-plate capacitor has uniform charge per unit area + on the upper plate and on the lower plate. The plates are horizontal, and both move horizontally with speed v to the right. (a) What is the magnetic field between the plates? (b) What is the magnetic field just above or just below the plates? (c) What are the magnitude and direction of the magnetic force per unit area on the upper plate? (d) At what extrapolated speed v will the magnetic force on a plate balance the electric force on the plate? Suggestion: Use Amperes law and choose a path that closes between the plates of the capacitor.
(a) Aircraft sometimes acquire small static charges, Suppose a supersonic jet has a 0.500C charge and flies due west at a speed of 660.m/s over Earth’s south magnetic pole, where the 8.00105T -T magnetic field points straight down into the ground, What are the direction and the magnitude of the magnetic force on the plane? fb) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect,

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