28. Magnetic Fields and Forces

A 5-m current-carrying wire (red line) is ran through a 4 T magnetic field (blue lines), as shown. The angle shown is 30°. What must the magnitude and direction of the current in the wire be when it feels a 3 N force directed into the page?

A small but rigid U-shaped wire carrying a 5.0-A current (Fig. 28–67) is placed inside a solenoid. The solenoid is 15.0 cm long and has 600 loops of wire, and the current in each loop is 7.0 A. What is the net force on the U-shaped wire?

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(I) (a) What is the force per meter of length on a straight wire carrying a 7.40-A current when perpendicular to a 0.90-T uniform magnetic field? (b) What if the angle between the wire and field is 35.0°?

(I) The magnetic force per meter on a wire is measured to be only 55% of its maximum possible value. What is the angle between the wire and the magnetic field?

A bolt of lightning strikes a metal flag pole, one end of which is anchored in the ground. Estimate the force the Earth’s magnetic field can exert on the flag pole while the lightning-induced current flows. See Example 25–10.

Near the equator, the Earth’s magnetic field points almost horizontally to the north and has magnitude B = 0.50 x 10⁻⁴ T. What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?

(II) A stiff wire 50.0 cm long is bent at a right angle in the middle. One section lies along the z axis and the other is along the line y = 2x in the xy plane. A current of 20.0 A flows in the wire—down the z axis and out the wire in the xy plane. The wire passes through a uniform magnetic field given by B (→ above B) = (0.285î ) T. Determine the magnitude and direction of the total force on the wire.

(II) The force on a wire carrying 6.45 A is a maximum of 1.64 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?

The power cable for an electric trolley (Fig. 27–60) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field has a strength 5.0 x 10⁻⁵ T and makes an angle of dip of 22° at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.

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(II) A current-carrying circular loop of wire (radius r, current I) is partially immersed in a magnetic field of constant magnitude B₀ directed out of the page as shown in Fig. 27–43. Determine the net force on the loop due to the field in terms of θ₀. (Note that θ₀ points to the dashed line, above which B = 0 .)

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(III) A curved wire, connecting two points a and b, lies in a plane perpendicular to a uniform magnetic field B (→ above B) and carries a current I. Show that the resultant magnetic force on the wire, no matter what its shape, is the same as that on a straight wire connecting the two points carrying the same current I. See Fig. 27–44.

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A uniform conducting rod of length ℓ and mass m sits atop a fulcrum, which is placed a distance ℓ/4 from the rod’s left-hand end and is immersed in a uniform magnetic field of magnitude B directed into the page (Fig. 27–54). An object whose mass M is 7.0 times greater than the rod’s mass is hung from the rod’s left-hand end. What current (direction and magnitude) should flow through the rod in order for it to be “balanced” (i.e., be at rest horizontally) on the fulcrum? (Flexible connecting wires which exert negligible force on the rod are not shown.)

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