22.11 More Applications of Magnetism

To see why an MRI utilizes iron to increase the magnetic field created by a coil, calculate the current needed in a 400-loop-per-meter circular coil 0.660 m in radius to create a 1.20-T field (typical of an MRI instrument) at its center with no iron present. The magnetic field of a proton is approximately like that of a circular current loop $0 . \text{650} \times \text{10}^{- \text{15}} m$ in radius carrying $1 . \text{05} \times \text{10}^{4} A$. What is the field at the center…

Nonnuclear submarines use batteries for power when submerged. (a) Find the magnetic field 50.0 cm from a straight wire carrying 1200 A from the batteries to the drive mechanism of a submarine. (b) What is the field if the wires to and from the drive mechanism are side by side? (c) Discuss the effects this could have for a compass on the submarine that is not shielded.

What current is needed in the solenoid described in the exercise to produce a magnetic field $\text{10}^{4}$ times the Earth’s magnetic field of $5 . \text{00} \times \text{10}^{- 5} T$?

Measurements affect the system being measured, such as the current loop in the reference. (a) Estimate the field the loop creates by calculating the field at the center of a circular loop 20.0 cm in diameter carrying 5.00 A. (b) What is the smallest field strength this loop can be used to measure, if its field must alter the measured field by less than 0.0100%?

Find the magnitude and direction of the magnetic field at the point equidistant from the wires in the reference(a), using the rules of vector addition to sum the contributions from each wire.

What current is needed in the top wire in the reference(a) to produce a field of zero at the point equidistant from the wires, if the currents in the bottom two wires are both 10.0 A into the page?

Find the radius of curvature of the path of a 25.0-MeV proton moving perpendicularly to the 1.20-T field of a cyclotron.

(a) Using the values given for an MHD drive in the exercise, and assuming the force is uniformly applied to the fluid, calculate the pressure created in $\text{N}/\text{m}^{2} .$ (b) Is this a significant fraction of an atmosphere?

A current balance used to define the ampere is designed so that the current through it is constant, as is the distance between wires. Even so, if the wires change length with temperature, the force between them will change. What percent change in force per degree will occur if the wires are copper?

A cyclotron accelerates charged particles as shown in the figure. Using the results of the previous problem, calculate the frequency of the accelerating voltage needed for a proton in a 1.20-T field.

(a) What is the direction of the force on a wire carrying a current due east in a location where the Earth’s field is due north? Both are parallel to the ground. (b) Calculate the force per meter if the wire carries 20.0 A and the field strength is $3 . \text{00} \times \text{10}^{- 5} T$. (c) What diameter copper wire would have its weight supported by this force? (d) Calculate the resistance per meter and the voltage per meter needed…

(a) Find the charge on a baseball, thrown at 35.0 m/s perpendicular to the Earth’s $5 . \text{00} \times \text{10}^{- 5} T$ field, that experiences a 1.00-N magnetic force. (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

An inventor wants to generate 120-V power by moving a 1.00-m-long wire perpendicular to the Earth’s $5 . \text{00} \times \text{10}^{- 5} T$ field. (a) Find the speed with which the wire must move. (b) What is unreasonable about this result? (c) Which assumption is responsible?

A surveyor 100 m from a long straight 200-kV DC power line suspects that its magnetic field may equal that of the Earth and affect compass readings. (a) Calculate the current in the wire needed to create a $5 . \text{00} \times \text{10}^{- 5} T$ field at this distance. (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

A magnetic field of $2.00 \times 10^{−7} \text{T}$ in the positive x-direction exists. Three electrons pass through the origin, one at a time, each with a velocity of $5.00 \times 10^{7} \text{m}/\text{s}$. The first electron passes the origin along the x-axis, the second electron along the y-axis, and the third at an angle of $45 °$ with respect to both the y- and z-axes in the yz-plane. (a) What is the force acting on each electron? (b) What is the shape of the pa…