Exam 20: Magnetism

An ideal solenoid that is $34.0 \mathrm {~cm}$ long is carrying a current of $2.00 \mathrm {~A}$ . If the magnitude of the magnetic field generated at the center of the solenoid is $9.00 \mathrm { mT }$ , how many turns of wire does this solenoid contain? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

The magnetic field at point P due to a 2.0-A current flowing in a long, straight, thin wire is $8.0 \mu T$ . How far is point $P$ from the wire? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

A positive charge is moving to the right and experiences an upward magnetic force, as shown in the figure. In which direction must the magnetic field have a component?

A flat rectangular loop of wire carrying a $4.0$ -A current is placed in a uniform $0.60 - T$ magnetic field. The magnitude of the torque acting on this loop when the plane of the loop makes a $30 ^ { \circ }$ angle with the field is measured to be $1.1 \mathrm {~N} \cdot \mathrm { m }$ . What is the area of this loop?

A proton moving at $5.0 \times 10 ^ { 4 } \mathrm {~m} / \mathrm { s }$ horizontally enters a region where a magnetic field of $0.12 \mathrm {~T}$ is present, directed vertically downward. What magnitude force acts on the proton due to this field? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A proton having a speed of $3.0 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$ in a direction perpendicular to a uniform magnetic field moves in a circle of radius $0.20 \mathrm {~m}$ within the field. What is the magnitude of the magnetic field? $( e$ $= 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ )

In a certain velocity selector consisting of perpendicular electric and magnetic fields, the charged particles move toward the east, and the magnetic field is directed to the north. What direction Should the electric field point?

A proton, with mass $1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ and charge $+ 1.6 \times 10 ^ { - 19 } \mathrm { C }$ , is sent with velocity $2.3 \times 10 ^ { 4 } \mathrm {~m} / \mathrm { s }$ in the $+ x$ direction into a region where there is a uniform electric field of magnitude $780 \mathrm {~V} / \mathrm { m }$ in the $+ y$ direction. What must be the magnitude and direction of the uniform magnetic field in the region if the proton is to pass through undeflected? Assume that the magnetic field has no $x$ component and neglect gravitational effects.

An electron is accelerated from rest through a potential difference of $3.75 \mathrm { kV }$ . It enters a region where a uniform 4.0-mT magnetic field is perpendicular to the velocity of the electron. Calculate the radius of the path this electron will follow in the magnetic field. $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = \right.$ $9.11 \times 10 ^ { - 31 } \mathrm {~kg}$ )

A flat circular coil has 250 identical loops of very thin wire. Each loop has an area of $0.12$ $\mathrm { m } ^ { 2 }$ and carries $15 \mathrm {~mA}$ of current. This coil is placed in a magnetic field of $0.050 \mathrm {~T}$ oriented at $30 ^ { \circ }$ to the plane of the loop. What is the magnitude of the magnetic moment of the coil?

Two long parallel wires are placed side-by-side on a horizontal table. If the wires carry current in the same direction,

A charged particle moves with a constant speed through a region where a uniform magnetic field is present. If the magnetic field points straight upward, the magnetic force acting on this particle Will be strongest when the particle moves

A charged particle is observed traveling in a circular path of radius R in a uniform magnetic field. If the particle were traveling twice as fast, the radius of the circular path would be

At point $P$ the magnetic field due to a long straight wire carrying a current of $2.0 \mathrm {~A}$ is $1.2 \mu \mathrm { T }$ . How far is $P$ from the wire? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

An ideal solenoid of length $10 \mathrm {~cm}$ consists of a wire wrapped tightly around a wooden core. The magnetic field strength is $4.0 \mathrm {~T}$ inside the solenoid. If the solenoid is stretched to $25 \mathrm {~cm}$ by applying a force to it, what does the magnetic field become?

An ideal solenoid is wound with 470 turns on a wooden form that is $4.0 \mathrm {~cm}$ in diameter and $50 \mathrm {~cm}$ Iong. The windings carry a current in the sense shown in the figure. The current produces a magnetic field of magnitude $4.1 \mathrm { mT }$ , at the center of the solenoid. What is the current $I$ in the solenoid windings? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

An electron moves with a speed of $8.0 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$ along the $+ x$ -axis. It enters a region where there is a magnetic field of $2.5 \mathrm {~T}$ , directed at an angle of $60 ^ { \circ }$ to the $+ x$ -axis and lying in the $x y$ -plane. Calculate the magnitude of the acceleration of the electron. $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { e 1 } = 9.11 \times 10 ^ { - 31 } \right.$ $\mathrm { kg }$ )

Two long parallel wires are placed side-by-side on a horizontal table and carry current in the same direction. The current in one wire is 20 A, and the current in the other wire is 5 A. If the Magnetic force on the 20-A wire has magnitude F, what is the magnitude of the magnetic force on The 5-A wire? No external magnetic fields are present.

A straight wire carries a current of 10 A at an angle of 30° with respect to the direction of a uniform 0.30-T magnetic field. Find the magnitude of the magnetic force on a 0.50-m length of the wire.

Two long parallel wires that are $0.30 \mathrm {~m}$ apart carry currents of $5.0 \mathrm {~A}$ and $8.0 \mathrm {~A}$ in the opposite direction. Find the magnitude of the force per unit length that each wire exerts on the other wire and indicate if the force is attractive or repulsive. $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$