What will be the current in the motor of the given example if the load causes it to run at half speed?

An enclosed transformer has four wire leads coming from it. How could you determine the ratio of turns on the two coils without taking the transformer apart?

An enclosed transformer has four wire leads coming from it. How would you know which wires paired with which?

A single point charge q is moving with velocity $\overrightarrow{\mathbf{v}}$. Use the Biot-Savart law to show that the magnetic field $\overrightarrow{\mathbf{B}}$ it produces at a point P, whose position vector relative to the charge is $\overrightarrow{\mathbf{r}}$, is given by

$$\overrightarrow{\mathbf{B}}=\frac{\mu_0}{4 \pi} \frac{q \overrightarrow{\mathbf{v}} \times \overrightarrow{\mathbf{r}}}{r^3}$$

(Assume v is much less than the speed of light.)

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?

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?

What is the value of the expression

$$\frac { 2 ^ { 3 } \cdot 4 - ( - 3 ) ^ { 2 } } { ( - 3 ) ^ { 2 } + 4 \cdot 5 } ?$$

$$F. \frac { 23 } { 29 }\quad G. \frac { 41} { 29 }\quad H. \frac { 23 } { 11} \quad I. \frac { 41} { 11 }$$

A wire, in a plane, has the shape shown in the given figure, two arcs of a circle connected by radial lengths of wire. Determine $\overrightarrow{\mathbf{B}}$ at point C in terms of $R_1, R_2, \theta$, and the current I.

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 would you do to the rotation frequency in order to double the rms voltage output?

Two long wires are oriented so that they are perpendicular to each other. At their closest, they are $20.0 \mathrm{~cm}$ apart (Fig. 28-39). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of $20.0 \mathrm{~A}$ and the bottom one carries $12.0 \mathrm{~A}$ ?

$$I_{\mathrm{T}}=20.0 \mathrm{~A}$$

A $20.0 \mathrm{~m}$ long copper wire, $2.00 \mathrm{~mm}$ in diameter including insulation, is tightly wrapped in a single layer with adjacent loops touching, to form a solenoid of diameter $2.50 \mathrm{~cm}$ (outer edge). What is the length of the solenoid?

A 20.0-m-long copper wire, $2.00 \mathrm{~mm}$ in diameter including insulation, is tightly wrapped in a single layer with adjacent coils touching, to form a solenoid of diameter $2.50 \mathrm{~cm}$ (outer edge). What is $(a)$ the length of the solenoid ?

A long horizontal wire carries $24.0 \mathrm{~A}$ of dc current due north. What is the net magnetic field $20.0 \mathrm{~cm}$ due west of the wire if the Earth's field there points downward, $38^{\circ}$ below the horizontal, and has magnitude $5.0 \times 10^{-5} \mathrm{~T}$ ?

A circular coil $18.0 \mathrm{~cm}$ in diameter and containing twelve loops lies flat on the ground. The Earth's magnetic field at this location has magnitude $5.50 \times 10^{-5} \mathrm{~T}$ and points into the Earth at an angle of $54.0^{\circ}$ below a line pointing due north. If a $7.10 \mathrm{~A}$ clockwise current passes through the coil, determine the torque on the coil.