Calculate the peak output voltage of a simple generator whose square armature windings are $5.50 \mathrm{~cm}$ on a side; the armature contains $125$ loops and rotates in a field of $0.200 \mathrm{~T}$ at a rate of $120 \mathrm{rev} / \mathrm{s}$.

In Fig. 29-12a, the rod moves to the right with a speed of $1.3 \mathrm{~m} / \mathrm{s}$ and has a resistance of $2.5 \Omega$. The rail separation is $\ell=25.0 \mathrm{~cm}$. The magnetic field is $0.35 \mathrm{~T}$, and the resistance of the U-shaped conductor is $25.0 \Omega$ at a given instant. Calculate (b) the current in the U-shaped conductor.

Suppose that the U-shaped conductor and connecting rod in Fig. 29-12a are oriented vertically (but still in contact) so that the rod is falling due to the gravitational force. Find the terminal speed of the rod if it has mass $m=3.6$ grams, length $\ell=18 \mathrm{~cm}$, and resistance $R=0.0013 \Omega$. It is falling in a uniform horizontal field $B=0.060 \mathrm{~T}$. Neglect the resistance of the U-shaped conductor.

In Fig. 29-12a, the rod moves to the right with a speed of $1.3 \mathrm{~m} / \mathrm{s}$ and has a resistance of $2.5 \Omega$. The rail separation is $\ell=25.0 \mathrm{~cm}$. The magnetic field is $0.35 \mathrm{~T}$, and the resistance of the U-shaped conductor is $25.0 \Omega$ at a given instant. Calculate (a) the induced emf.

A circular loop in the plane of the paper lies in a $0.65~\mathrm{T}$ uniform magnetic field pointing into the paper. The loop's diameter changes from $20.0 \mathrm{~cm}$ to $8.0 \mathrm{~cm}$ in $0.50 \mathrm{~s}$. What is the average induced current if the coil resistance is $2.5 \Omega$ ?

A circular current loop of radius $15 \mathrm{~cm}$ containing $220$ turns carries a current of $2.0 \mathrm{~A}$. Its center is at the origin and its axis lies along the $x$ axis. Calculate the magnetic field $B$ at a point $x$ on the $x$ axis for $x=-40 \mathrm{~cm}$ to $+40 \mathrm{~cm}$ in steps of $2 \mathrm{~cm}$ and make a graph of $B$ as a function of $x$.

A circular loop in the plane of the paper lies in a $0.65~\mathrm{T}$ uniform magnetic field pointing into the paper. The loop's diameter changes from $20.0 \mathrm{~cm}$ to $8.0 \mathrm{~cm}$ in $0.50 \mathrm{~s}$. What is the magnitude of the average induced emf?

A circular loop in the plane of the paper lies in a $0.65~\mathrm{T}$ uniform magnetic field pointing into the paper. The loop's diameter changes from $20.0 \mathrm{~cm}$ to $8.0 \mathrm{~cm}$ in $0.50 \mathrm{~s}$. What is the direction of the induced current?

The magnetic field perpendicular to a single $13.2~\mathrm{cm}$ diameter circular loop of copper wire decreases uniformly from $0.760 \mathrm{~T}$ to zero. If the wire is $2.25 \mathrm{~mm}$ in diameter, how much charge moves past a point in the coil during this operation?

A third wire is placed in the plane of the two wires shown in the given figure parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.

In a physics laboratory experiment, a coil with 200 turns enclosing an area of $12 ~\mathrm{cm}^{2}$ is rotated in 0.040 s from a position where its plane is perpendicular to the earth’s magnetic field to a position where its plane is parallel to the field. The earth’s magnetic field at the lab location is $6.0 \times 10^{-5} ~\mathrm{T}$. What is the total magnetic flux through the coil before it is rotated? After it is rotated?

If the resistance of the resistor in the given figure is slowly increased, what is the direction of the current induced in the small circular loop inside the larger loop?

A circular wire loop of radius $r=12 \mathrm{~cm}$ is in a uniform magnetic field $B=0.400 \mathrm{~T}$ with its plane perpendicular to the direction of the field. If the field magnitude begins to decrease at a rate of $-0.010 \mathrm{~T} / \mathrm{s}$, at what rate should $r$ be increasing at this instant so that the induced emf within the loop is zero?

A long copper strip is $3.0 \mathrm{~cm}$ wide and $1.0 \mathrm{~mm}$ thick. When it carries a steady $42~ \mathrm{A}$ current in a $0.80~ \mathrm{T}$ magnetic field it produces a $6.5~\mu \mathrm{V}$ Hall emf. Determine the Hall field in the conductor.