Chapter 29: The Magnetic Field

At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your answer as a multiple of R.

At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your fanswer as a multiple of $R$.

Find an expression for the magnetic field strength at the center (point P) of the circular arc in $FIGUREP29.45.$

$FIGUREP29.45$ localid="1649251364548" $FIGUREP29.46$

Find an expression for the magnetic field strength at the center $(pointP)$of the circular arc in FIGURE P29.45.

What are the strength and direction of the magnetic field at point P in FIGURE P29.46?

A scientist measuring the resistivity of a new metal alloy left her ammeter in another lab, but she does have a magnetic field probe. So she creates a $6.5m$long, $2.0mm$-diameter wire of the material, connects it to a $1.5V$battery, and measures a $3.0mT$ magnetic field $1.0mm$ from the surface of the wire. What is the material’s resistivity?

A $2.5$-m-long, $2.0$-mm-diameter aluminum wire has a potential difference of $1.5V$ between its ends. Consider an electron halfway between the center of the wire and the surface that is moving parallel to the wire at the drift speed. What is the ratio of the electric force on the electron to the magnetic force on the electron?

Your employer asks you to build a $20$-cm-long solenoid with an interior field of $5.0mT$. The specifications call for a single layer of wire, wound with the coils as close together as possible. You have two spools of wire available. Wire with a $\#18$gauge has a diameter of $1.02mm$and has a maximum current rating of $6A$. Wire with a $\#26$gauge is $0.41mm$in diameter and can carry up to $1A$. Which wire should you use, and what current will you need?

What is the current direction in the wire of FIGURE Q29.5? Explain.

What is the magnetic field at the position of the dot in FIGURE EX29.5? Give your answer as a vector.