Chapter 19, Magnetic Fields Ii Video Solutions, Electromagnetic Fields and Waves: Including Electric Circuits

Problem 1

The vector potential inside a current-carrying conductor Show that, inside a straight current-carrying conductor of radius $R$,
$$
A=\frac{\mu_{0} I}{4 \pi}\left(1-\frac{\rho^{2}}{R^{2}}\right)
$$
if $A$ is set equal to zero at $\rho=R$.

- -

Numerade Educator

01:01

Problem 2

Van de Graaff high-voltage generator
In a Van de Graaff generator, a charged insulating belt transports electric charge to the high-voltage electrode.
(a) Calculate the current carried by a 500 -millimeter-wide belt driven by a 100 -millimeter-diameter pulley that rotates at 60 revolutions/second, if $E=2 \times 10^{\circ}$ volts/meter at the surface of the belt.
(b) Calculate the $B$ close to the belt.

Shahab Ullah

Numerade Educator

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Problem 3

The toroidal coil
Figure $19-8$ shows a toroidal coil of square cross section. There are $N$ turns, and the current is $I$.
Find (a) the azimuthal field along paths $a$ and $c$, (b) $B$ inside the toroid, and (c) the line integral of $B$ along path $d$.

Eduard Sanchez

Numerade Educator

01:16

Problem 4

$\boldsymbol{B}$ near a conducting sheet
A conducting sheet carries a current density of $\alpha$ amperes/meter. There are no other currents in the vicinity.
(a) What is the value of $B$, close to the sheet?
(b) How is $\boldsymbol{B}$ oriented with respect to $\alpha$ ?
(c) A conducting body carries a high-frequency current that is confined near the surface. The surface current density is $a$ amperes/meter. Show that, in the air ncar the conductor, $B=\mu_{0} \alpha \times \hat{n}$, where $\hat{n}$ is a unit vector normal to the surface and pointing outward.

Zulfiqar Ali

Numerade Educator

01:01

Problem 5

The magnetic ficld near the axis of a circular loop
A circular loop carries a current $I$. Choose the axis of symmetry as the $z$-axis, and calculate $B_{\rho}$ and $B_{z}$ near the axis.

Narayan Hari

Numerade Educator

01:03

Problem 6

The average $\boldsymbol{B}$ over a sphere is equal to $\boldsymbol{B}$ at the center Refer to Prob. 3-16 concerning the average $E$ over a spherical volume. Show that, in a region where there are no currents, the average $B$ over a spherical volume is equal to the $\boldsymbol{B}$ at the center.

Nick Johnson

Numerade Educator

02:28

Problem 7

(19.5) The field of a short thick solenoid, compared to that of a long solenoid

The value of $B$ at the center of a short, thick solenoid given in Prob. 18-7 can be written as $B=\mu_{0} N^{\prime} I g$, where $\mu_{0} N^{\prime} I$ is the field of a long solenoid. Find $g$.

Manish Kumar ( Iit K )

Numerade Educator