A dc motor has an armature resistance of $2.65 \Omega$. If it draws $7.20 \mathrm{~A}$ when running at full speed and connected to a $120~\mathrm{V}$ line, how large is the back emf?

A $280$-loop circular armature coil with a diameter of $10.0 \mathrm{~cm}$ rotates at $120 \mathrm{rev} / \mathrm{s}$ in a uniform magnetic field of strength $0.45 \mathrm{~T}$. What is the rms voltage output of the generator?

Which of the following can a transformer accomplish? $(a)$ Changing voltage but not current. $(b)$ Changing current but not voltage. $(c)$ Changing power. $(d)$ Changing both current and voltage.

A particle of charge q moves in a circular path of radius r in a uniform magnetic field B. Show that its momentum is $p=q B r$.

A long wire stretches along the $x$ axis and carries a $3.0 \mathrm{~A}$ current to the right $(+x)$. The wire is in a uniform magnetic field $\overrightarrow{\mathbf{B}}=(0.20 \hat{\mathbf{i}}-0.42 \hat{\mathbf{j}}+0.25 \hat{\mathbf{k}}) \mathrm{T}$. Determine the components of the force on the wire per $\mathrm{cm}$ of length.

A long wire stretches along the $x$ axis and carries a $3.0-\mathrm{A}$ current to the right $(+x)$. The wire is in a uniform magnetic field $\overrightarrow{\mathbf{B}}=(0.20 \hat{\mathbf{i}}-0.36 \hat{\mathbf{j}}+0.25 \hat{\mathbf{k}}) \mathrm{T}$. Determine the components of the force on the wire per $\mathrm{cm}$ of length.

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.

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.

Expand each of the following functions in a Fourier sine series on the prescribed interval. $f(x)=e^{-x} ; \quad 0<x<1$

The area of an elastic circular loop decreases at a constant rate, $d A / d t=-3.50 \times 10^{-2} \mathrm{~m}^2 / \mathrm{s}$. The loop is in a magnetic field $B=0.28 \mathrm{~T}$ whose direction is perpendicular to the plane of the loop. At $t=0$, the loop has area $A=0.285 \mathrm{~m}^2$. Determine the induced emf at $t=0$, and at $t=2.00 \mathrm{~s}$.

A 16-cm-diameter circular loop of wire is placed in a $0.50-\mathrm{T}$ magnetic field. (b) The plane of the lop is rotated until it makes a $35^{\circ}$ angle with the field lines. What is the angle $\theta$ in Eq. 29-1a for this situation?

A 16-cm-diameter circular loop of wire is placed in a $0.50-\mathrm{T}$ magnetic field. (a) When the plane of the loop is perpendicular to the field lines, what is the magnetic flux through the loop?

A 16-cm-diameter circular loop of wire is placed in a $0.50-\mathrm{T}$ magnetic field. (c) What is the magnetic flux through the loop at this angle?

The wire of a tightly wound solenoid is unwound and used to make another tightly wound solenoid of twice the diameter. By what factor does the inductance change?