Chapter 29

A surveyor is using a magnetic compass \(6.1 \mathrm{~m}\) below a power line in which there is a steady current of 100 A. (a) What is the magnetic field at the site of the compass due to the power line? (b) Will this field interfere seriously with the compass reading? The horizontal component of Earth's magnetic field at the site is \(20 \mu \mathrm{T}\).

SSM At a certain location in the Philippines, Earth's magnetic field of \(39 \mu \mathrm{T}\) is horizontal and directed due north. Suppose the net field is zero exactly \(8.0 \mathrm{~cm}\) above a long, straight, horizontal wire that carries a constant current. What are the (a) magnitude and (b) direction of the current?

Equation \(29-4\) gives the magnitude \(B\) of the magnetic field set up by a current in an infinitely long straight wire, at a point \(P\) at perpendicular distance \(R\) from the wire. Suppose that point \(P\) is actually at perpendicular distance \(R\) from the midpoint of a wire with a finite length \(L\). Using Eq. \(29-4\) to calculate \(B\) then results in a certain percentage error. What value must the ratio \(L / R\) exceed if the percentage error is to be less than \(1.00 \%\) ? That is, what \(L / R\) gives

One long wire lies along an \(x\) axis and carries a current of 30 A in the positive \(x\) direction. A second long wire is perpendicular to the \(x y\) plane, passes through the point \((0,4.0 \mathrm{~m}, 0)\), and carries a current of \(40 \mathrm{~A}\) in the positive \(z\) direction. What is the magnitude of the resulting magnetic field at the point \((0,2.0 \mathrm{~m}, 0)\) ?

\(.\) ILW Figure 29-51 shows a snapshot of a proton moving at velocity \(\vec{v}=(-200 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{j}}\) toward a long straight wire with current \(i=350 \mathrm{~mA} .\) At the instant shown, the proton's distance from the wire is \(d=2.89 \mathrm{~cm} .\) In unitvector notation, what is the magnetic force on the proton due to the current?

The current density \(\vec{J}\) inside a long, solid, cylindrical wire of radius \(a=3.1 \mathrm{~mm}\) is in the direction of the central axis, and its magnitude varies linearly with radial distance \(r\) from the axis according to \(J=J_{0} r / a\), where \(J_{0}=\) \(310 \mathrm{~A} / \mathrm{m}^{2}\). Find the magnitude of the magnetic field at (a) \(r=0\), (b) \(r=a / 2\), and (c) \(r=a\).

A toroid having a square cross section, \(5.00 \mathrm{~cm}\) on a side, and an inner radius of \(15.0 \mathrm{~cm}\) has 500 turns and carries a current of \(0.800\) A. (It is made up of a square solenoid-instead of a round one as in Fig. \(29-17\) -bent into a doughnut shape.) What is the magnetic field inside the toroid at (a) the inner radius and (b) the outer radius?

A solenoid that is \(95.0 \mathrm{~cm}\) long has a radius of \(2.00 \mathrm{~cm}\) and a winding of 1200 turns; it carries a current of \(3.60\) A. Calculate the magnitude of the magnetic field inside the solenoid.

A 200-turn solenoid having a length of \(25 \mathrm{~cm}\) and a diameter of \(10 \mathrm{~cm}\) carries a current of \(0.29\) A. Calculate the magnitude of the magnetic field \(\vec{B}\) inside the solenoid.

A long solenoid has 100 turns/cm and carries current \(i\). An electron moves within the solenoid in a circle of radius \(2.30 \mathrm{~cm}\) perpendicular to the solenoid axis. The speed of the electron is \(0.0460 c(c=\) speed of light \() .\) Find the current \(i\) in the solenoid.

A long solenoid with \(10.0\) turns \(/ \mathrm{cm}\) and a radius of \(7.00 \mathrm{~cm}\) carries a current of \(20.0 \mathrm{~mA}\). A current of \(6.00 \mathrm{~A}\) exists in a straight conductor located along the central axis of the solenoid. (a) At what radial distance from the axis will the direction of the resulting magnetic field be at \(45.0^{\circ}\) to the axial direction? (b) What is the magnitude of the magnetic field there?

A student makes a short electromagnet by winding 300 turns of wire around a wooden cylinder of diameter \(d=5.0 \mathrm{~cm}\). The coil is connected to a battery producing a current of \(4.0 \mathrm{~A}\) in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance \(z \geqslant d\) will the magnetic field have the magnitude \(5.0 \mu \mathrm{T}\) (approximately one-tenth that of Earth's magnetic field)?

A circular loop of radius \(12 \mathrm{~cm}\) carries a current of \(15 \mathrm{~A}\). A flat coil of radius \(0.82 \mathrm{~cm}\), having 50 turns and a current of \(1.3 \mathrm{~A}\), is concentric with the loop. The plane of the loop is perpendicular to the plane of the coil. Assume the loop's magnetic field is uniform across the coil. What is the magnitude of (a) the magnetic field produced by the loop at its center and (b) the torque on the coil due to the loop?

Two long wires lie in an \(x y\) plane, and each carries a current in the positive direction of the \(x\) axis. Wire 1 is at \(y=10.0 \mathrm{~cm}\) and carries \(6.00 \mathrm{~A}\); wire 2 is at \(y=5.00 \mathrm{~cm}\) and carries \(10.0 \mathrm{~A}\). (a) In unitvector notation, what is the net magnetic field \(\vec{B}\) at the origin? (b) At what value of \(y\) does \(\vec{B}=0 ?(\mathrm{c})\) If the current in wire 1 is reversed, at what value of \(y\) does \(\vec{B}=0 ?\)

Two wires, both of length \(L\), are formed into a circle and a square, and each carries current \(i\). Show that the square produces a greater magnetic field at its center than the circle produces at its center.

A long straight wire carries a current of \(50 \mathrm{~A} .\) An electron, traveling at \(1.0 \times 10^{7} \mathrm{~m} / \mathrm{s}\), is \(5.0 \mathrm{~cm}\) from the wire. What is the magnitude of the magnetic force on the electron if the electron velocity is directed (a) toward the wire, (b) parallel to the wire in the direction of the current, and (c) perpendicular to the two directions defined by (a) and (b)?

A long vertical wire carries an unknown current. Coaxial with the wire is a long, thin, cylindrical conducting surface that carries a current of \(30 \mathrm{~mA}\) upward. The cylindrical surface has a radius of \(3.0 \mathrm{~mm}\). If the magnitude of the magnetic field at a point \(5.0 \mathrm{~mm}\) from the wire is \(1.0 \mu \mathrm{T}\), what are the (a) size and (b) direction of the current in the wire?

The magnitude of the magnetic field at a point \(88.0 \mathrm{~cm}\) from the central axis of a long straight wire is \(7.30 \mu \mathrm{T}\). What is the current in the wire?

Go Figure \(29-82\) shows, in cross section, two long parallel wires spaced by distance \(d=10.0 \mathrm{~cm} ;\) each carries \(100 \mathrm{~A}\), out of the page in wire 1. Point \(P\) is on a perpendicular bisector of the line connecting the wires. In unit-vector notation, what is the net magnetic field at \(P\) if the current in wire 2 is (a) out of the page and (b) into the page?

A long, hollow, cylindrical conductor (with inner radius \(2.0\) \(\mathrm{mm}\) and outer radius \(4.0 \mathrm{~mm}\) ) carries a current of 24 A distributed uniformly across its cross section. A long thin wire that is coaxial with the cylinder carries a current of \(24 \mathrm{~A}\) in the opposite direction. What is the magnitude of the magnetic field (a) \(1.0 \mathrm{~mm}\), (b) \(3.0 \mathrm{~mm}\), and (c) \(5.0 \mathrm{~mm}\) from the central axis of the wire and cylinder?

A long wire is known to have a radius greater than \(4.0 \mathrm{~mm}\) and to carry a current that is uniformly distributed over its cross section. The magnitude of the magnetic field due to that current is \(0.28 \mathrm{mT}\) at a point \(4.0 \mathrm{~mm}\) from the axis of the wire, and \(0.20 \mathrm{mT}\) at a point 10 \(\mathrm{mm}\) from the axis of the wire. What is the radius of the wire?