# Talk:QB/d cp2.12

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Free space permeability $\mu _{0}=4\pi \times 10^{-7}$ T·m/A
Force between parallel wires ${\tfrac {F}{\ell }}={\tfrac {\mu _{0}I_{1}I_{2}}{2\pi r}}$ Biot–Savart law ${\vec {B}}={\tfrac {\mu _{0}}{4\pi }}\int \limits _{wire}{\frac {Id{\vec {\ell }}\times {\hat {r}}}{r^{2}}}$ Ampère's Law:$\oint {\vec {B}}\cdot d{\vec {\ell }}=4\pi \mu _{0}I_{enc}$ Magnetic field inside solenoid with paramagnetic material =$B=\mu nI$ where $\mu =(1+\chi )\mu _{0}$ = permeability

1. Example 12.s from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:dh0GjBEd@2/121-The-Biot-Savart-Law_1 A wire carries a current of 200 A in a circular arc with radius 2 cm swept through 40 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?}
2. Example 12.3 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:ltGE2kXG@3/122-Magnetic-Field-Due-to-a-Th_1
Three wires sit at the corners of a square of length 1 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.9 A, 2.0 A, 2.1 A), respectively. What is the x-component of the magnetic field at point P?}
3. Example 12.3 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:ltGE2kXG@3/122-Magnetic-Field-Due-to-a-Th_1
Three wires sit at the corners of a square of length 1 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.9 A, 2.0 A, 2.1 A), respectively. What is the y-component of the magnetic field at point P?}
4. Example 12.4 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:VY8a9ouJ@2/123-Magnetic-Force-between-Two_1 Two parallel wires each carry a 5.0 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.0 cm, 0.9 cm), while the other is located at (0.000E+00 cm, 4.0 cm). What is the force per unit length between the wires?
5. Example 12.5 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:A6AqGAGN@2/124-Magnetic-Field-of-a-Curren_1 Two loops of wire carry the same current of 10 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.5 m while the other has a radius of 1.0 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.25 m from the first (smaller) loopif the disance between the loops is 1.0 m?
6. Example 12.7 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:zDDQ_D36@2/125-Ampres-Law_1 Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 0.8 mm from the center of a wire of radius 2 mm if the current is 1A?
7. Example 12.6 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:zDDQ_D36@2/125-Ampres-Law_1 The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r  is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$  is the maximum magnetic field (at $r=a$ ). If $a=$  0.5 m and $B_{max}=\,$  0.3 T, then how much current (in the z-direction) flows through a circle of radius $r=$  0.25 m that is centered on the axis with its plane perpendicular to the axis?
8. Example 12.8 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:zDDQ_D36@2/125-Ampres-Law_1
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $\beta$  and $\omega$ . If I1=2.5 kA, I2=0.75 kA, and I3=1.5 kA, take the $\beta$  path and evalulate the line integral,
$\oint {\vec {B}}\cdot d{\vec {\ell }}$ :
9. Example 12.8 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:zDDQ_D36@2/125-Ampres-Law_1
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $\beta$  and $\omega$ . If I1=2.5 kA, I2=0.75 kA, and I3=1.5 kA, take the $\omega$  path and evalulate the line integral,
$\oint {\vec {B}}\cdot d{\vec {\ell }}$ :
10. Example 12.9 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:Xx_lDtUL@2/126-Solenoids-and-Toroids_1 A solenoid has 3.000E+04 turns wound around a cylinder of diameter 1.2 cm and length 14 m. The current through the coils is 0.41 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $\int {\vec {B}}\cdot {\vec {\ell }}$  alongthe axis from z=−2 cm to z=+8 cm
11. Example 12.10 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:_FueUvPK@4/127-Magnetism-in-Matter_1 A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 200 mA, the net magnetic field is measured to be 1.4 T. What is the magnetic susceptibility for this case?