Exam 20: Magnetism

In the figure, the two long straight wires are separated by a distance of $d = 0.40 \mathrm {~m}$ . The currents are $I _ { 1 } = 1.0 \mathrm {~A}$ to the right in the upper wire and $I _ { 2 } = 8.0 \mathrm {~A}$ to the left in the lower wire. What are the magnitude and direction of the magnetic field at point $P$ , that is a distance $d / 2 = 0.20 \mathrm {~m}$ below the lower wire? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

How many turns should a $10 - \mathrm { cm }$ long ideal solenoid have if it is to generate a $1.5 - \mathrm { mT }$ magnetic field when $1.0 \mathrm {~A}$ of current runs through it? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

A rectangular coil, with corners labeled $A B C D$ , has length $L$ and width $w$ . It is placed between the poles of a magnet, as shown in the figure. If there is a current $I$ flowing through this coil in the direction shown, what is the direction of the force acting on section CD of this coil?

At a particular instant, a proton moves toward the east in a uniform magnetic field that is directed straight downward. The magnetic force that acts on it is

In order to trap the starship Enterprise, the diabolical Klingons build a huge ideal solenoid 10 light-years long with a diameter of $2.0$ million kilometers. Every kilometer of length of the solenoid contains 100 turns of wire. What magnetic field strength is produced near the center of the solenoid using a current of $2.00 \mathrm { kA }$ ? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

At a particular instant, an electron moves toward the east in a uniform magnetic field that is directed straight downward. The magnetic force that acts on it is

An electron moving perpendicular to a uniform magnetic field of $3.2 \times 10 ^ { - 2 } \mathrm {~T}$ moves in a circle of radius $0.40 \mathrm {~cm}$ . How fast is this electron moving? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

A wire in the shape of an "M" lies in the plane of the paper. It carries a current of $2.0 \mathrm {~A}$ , flowing from $A$ to $E$ , as shown in the figure. It is placed in a uniform magnetic field of $0.55 \mathrm {~T}$ in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. Note that $A B$ is parallel to $D E$ and to the baseline from which the magnetic field direction is measured. What are the magnitude and direction of the force acting on section CD of this wire?

A straight wire that is $0.60 \mathrm {~m}$ and carrying a current of $2.0 \mathrm {~A}$ is placed at an angle with respect to the magnetic field of strength $0.30 \mathrm {~T}$ . If the wire experiences a force of magnitude $0.18 \mathrm {~N}$ , what angle does the wire make with respect to the magnetic field?

A rectangular coil, with corners labeled $\mathrm { ABCD }$ , has length $L$ and width $w$ . It is placed between the poles of a magnet, as shown in the figure If there is a current $I$ flowing through this coil in the direction shown, what is the direction of the force acting on section BC of this coil?

A horizontal wire carries a current straight toward you. From your point of view, the magnetic field caused by this current

A doubly charged ion with speed $6.9 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$ enters a uniform $0.80 - T$ magnetic field, traveling perpendicular to the field. Once in the field, it moves in a circular arc of radius $30 \mathrm {~cm}$ . What is the mass of this ion? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A flat square coil of wire measures $9.5 \mathrm {~cm}$ on each side and contains 175 turns of very thin wire. It carries a current of $6.3 \mathrm {~A}$ in a uniform 0.84-T magnetic field. What angle less than $90 ^ { \circ }$ should the plane of this coil make with the magnetic field direction so that the magnitude of the magnetic torque on it is $6.5 \mathrm {~N} \cdot \mathrm { m }$ ?

Two parallel straight wires are $7.0 \mathrm {~cm}$ apart and $50 \mathrm {~m}$ long. Each one carries a $18 - \mathrm { A }$ current in the same direction. One wire is securely anchored, and the other is attached in the center to a movable cart. If the force needed to move the wire when it is not attached to the cart is negligible, with what magnitude force does the wire pull on the cart? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

The magnetic field at a distance of $2 \mathrm {~cm}$ from a long straight current-carrying wire is $4 \mu T$ . What is the magnetic field at a distance of $4 \mathrm {~cm}$ from this wire?

If a calculated quantity has units of $\frac { \mathrm { N } \cdot \mathrm { s } } { \mathrm { C } \cdot \mathrm { m } }$ , that quantity could be

An ideal solenoid having a coil density of 5000 turns per meter is $10 \mathrm {~cm}$ long and carries a current of $4.0 \mathrm {~A}$ . What is the strength of the magnetic field at its center?

If a calculated quantity has units of $T \cdot \mathrm { m } / \mathrm { A }$ , that quantity could be

In the figure, the rectangular loop is pivoted about one side (of length $0.060 \mathrm {~m}$ ), that coincides with the $y$ -axis. The end (length $0.020 \mathrm {~m}$ ) of the loop that lies in the $x z -$ plane makes an angle of $37 ^ { \circ }$ with the $x$ -axis as shown. The loop carries a current of $I = 69 \mathrm {~A}$ in the direction shown. (In the side of the loop that is along the $y$ -axis the current is in the $+ y$ direction.) If there is a uniform magnetic field of magnitude $9.7 \mathrm {~T}$ in the $- x$ direction, find the magnitude of the torque that this magnetic field exerts on the loop.

A very long thin wire produces a magnetic field of $0.0020 \times 10 ^ { - 4 } \mathrm {~T}$ at a distance of $1.0 \mathrm {~mm}$ from the wire. What is the magnitude of the current? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$