Magnetism and the Electric Field

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[pic 33]

29-11. What if an electron replaces the proton in Problem 29-10. What is the magnitude and direction of the magnetic force?

The direction of the magnetic force on an electron is opposite to that of the proton, but the magnitude of the force is unchanged since the magnitude of the charge is the same.[pic 34]

Fe = 2.56 x 10-13 N, out of paper.

*29-12. A particle having a charge q and a mass m is projected into a B field directed into the paper. If the particle has a velocity v, show that it will be deflected into a circular path of radius:

[pic 35]

Draw a diagram of the motion, assuming a positive charge entering the B field from left to right. Hint: The magnetic force provides the necessary centripetal force for the circular motion.[pic 36]

[pic 37]

From which: [pic 38]

The diagram shows that the magnetic force is a centripetal force that acts toward the center causing the charge to move in a counterclockwise circle of radius R.

[pic 39]

*29-13. A deuteron is a nuclear particle consisting of a proton and a neutron bound together by nuclear forces. The mass of a deuteron is 3.347 x 10-27 kg, and its charge is +1e. A deuteron projected into a magnetic field of flux density 1.2 T is observed to travel in a circular path of radius 300 mm. What is the velocity of the deuteron? See Problem 29-12.

[pic 40]

[pic 41]; v = 1.72 x 107 m/s[pic 42]

Note: This speed which is about 6% of the speed of light is still not fast enough to cause significant effects due to relativity (see Chapter 38.)

Force on a Current-Carrying Conductor

29-14. A wire 1 m in length supports a current of 5.00 A and is perpendicular to a B field of 0.034 T. What is the magnetic force on the wire?[pic 43]

F = I B⊥ l= (5 A)(0.034 T)(1 m); F = 0.170 N

[pic 44]

29-15. A long wire carries a current of 6 A in a direction 350 north of an easterly 40-mT magnetic field. What are the magnitude and direction of the force on each centimeter of wire?[pic 45]

F = Il B sin θ = (6 A)(0.040 T)(0.01 m)sin 350[pic 46]

F = 1.38 x 10-3 N, into paper

The force is into paper as can be seen by turning I into B to advance a screw inward.

[pic 47]

29-16. A 12-cm segment of wire carries a current of 4.0 A directed at an angle of 410 north of an easterly B field. What must be the magnitude the B field if it is to produce a 5 N force on this segment of wire? What is the direction of the force?

[pic 48] B = 15.9 T[pic 49]

The force is directed inward according to the right-hand rule.

[pic 50]

29-17. An 80 mm segment of wire is at an angle of 530 south of a westward, 2.3-T B field. What are the magnitude and direction of the current in this wire if it experiences a force of 2 N directed out of the paper?[pic 51][pic 52][pic 53][pic 54][pic 55][pic 56][pic 57][pic 58]

B = 2.30 T; l = 0.080 m; θ = 530; F = 2.00 N[pic 59]

[pic 60] I = 13.6 A[pic 61]

The current must be directed 530 N of E if I turned into B produces outward force.

*29-18. The linear density of a certain wire is 50.0 g/m. A segment of this wire carries a current of 30 A in a direction perpendicular to the B field. What must be the magnitude of the magnetic field required to suspend the wire by balancing its weight?

[pic 62] FB = I lB

λlg = IlB; [pic 63]; B = 16.3 mT[pic 64]

Calculating Magnetic Fields

29-19. What is the magnetic induction B in air at a point 4 cm from a long wire carrying a current of 6 A?

[pic 65]; B = 30.0 μT[pic 66]

[pic 67]

29-20. Find the magnetic induction in air 8 mm from a long wire carrying a current of 14.0 A.

[pic 68]; B = 350 μT[pic 69]

[pic 70]

29-21. A circular coil having 40 turns of wire in air has a radius of 6 cm and is in the plane of the paper. What current must exist in the coil to produce a flux density of 2 mT at its center?

[pic 71]

[pic 72]; I = 4.77 A[pic 73]

29-22. If the direction of the current in the coil of Problem 29-21 is clockwise, what is the direction of the magnetic field at the center of the loop?[pic 74][pic 75][pic 76]

If you grasp the loop with your right hand so that the thumb[pic 77]

points in the direction of the current, it is seen that the B field

will be directed OUT of the paper at the center of the loop.

[pic 78]

29-23. A solenoid of length 30 cm and diameter 4 cm is closely wound with 400 turns of wire around a nonmagnetic material. If the current in the wire is 6 A, determine the magnetic induction along the center of the solenoid.

[pic 79]; B = 10.1 mT[pic 80][pic 81]

29-24. A circular coil having 60 turns has a radius of 75 mm. What current must exist in the coil to produce a flux density of 300 μT at the center of the coil?

[pic 82]; I = 0.597 A[pic 83]

[pic 84]

*29-25. A circular loop 240 mm in diameter supports a current of 7.8 A. If it is submerged in a medium of relative permeability 2.0, what is the magnetic induction at the center?

r = ½(240 mm) = 120 mm; μ = 2μ0 = 8π x 10-7 T m/A