# Talk:QB/d cp2.11

cross product

${\displaystyle |{\vec {a}}\times {\vec {b}}|}$${\displaystyle =ab\sin \theta \Leftrightarrow }$ ${\displaystyle ({\vec {a}}\times {\vec {b}})_{x}=(a_{y}b_{z}-a_{z}b_{y})}$, ${\displaystyle ({\vec {a}}\times {\vec {b}})_{y}=(a_{z}b_{x}-a_{x}b_{z})}$, ${\displaystyle ({\vec {a}}\times {\vec {b}})_{z}=(a_{x}b_{y}-a_{y}b_{x})}$
Magnetic force: ${\displaystyle {\vec {F}}=q{\vec {v}}\times {\vec {B}},\;}$${\displaystyle d{\vec {F}}=I{\overrightarrow {d\ell }}\times {\vec {B}}}$.
${\displaystyle {\vec {v}}_{d}={\vec {E}}\times {\vec {B}}/B^{2}}$=EXB drift velocity
Circular motion (uniform B field): ${\displaystyle r={\tfrac {mv}{qB}}.\;}$ Period=${\displaystyle T={\tfrac {2\pi m}{qB}}.\;}$

Hall effect

Dipole moment=${\displaystyle {\vec {\mu }}=NIA{\hat {n}}}$. Torque=${\displaystyle {\vec {\tau }}={\vec {\mu }}\times {\vec {B}}}$. Stored energy=${\displaystyle U={\vec {\mu }}\cdot {\vec {B}}}$.
Hall field =${\displaystyle E=V/\ell =Bv_{d}={\tfrac {IB}{neA}}}$
Lorentz force =${\displaystyle q\left({\vec {E}}+{\vec {v}}\times {\vec {B}}\right)}$

1. Example 11.1 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@14.1:KiBTyzfq@6/11-2-Magnetic-Fields-and-Lines An alpha-particle (q=3.2x10−19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 1.5 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(2.2 i + 3.3 j  + 1.1 k) x 104 m/s?
2. Example 11.2 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@14.1:KiBTyzfq@6/11-2-Magnetic-Fields-and-Lines A charged particle in a magnetic field of 1.000E-04 T is moving perpendicular to the magnetic field with a speed of 5.000E+05 m/s. What is the period of orbit if orbital radius is 0.5 m?
3. Example 11.2 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@14.1:bZRPyVNP@8/11-3-Motion-of-a-Charged-Particle-in-a-Magnetic-Field An alpha-particle (m=6.64x10−27kg, q=3.2x10−19C) briefly enters a uniform magnetic field of magnitude 0.05 T . It emerges after being deflected by 45° from its original direction. How much time did it spend in that magnetic field?
4. Example 11.4 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:BLPqsvDS@2/114-Magnetic-Force-on-a-Curren_1 A 50 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.5 T. What current is required to maintain this balance?
5. Example 11.5 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:BLPqsvDS@2/114-Magnetic-Force-on-a-Curren_1 A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.3 T magnetic field is directed 60° away from the wire?
6. Example 11.7 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:MSd97aoE@2/115-Force-and-Torque-on-a-Curr_1 A circular current loop of radius 2 cm carries a current of 2 mA. What is the magnitude of the torque if the dipole is oriented at 30 ° to a uniform magnetic fied of 0.5 T?
7. Example 11.8 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:kh61-j3_@2/116-The-Hall-Effect_1 An electron beam (m=9.1 x 10−31kg, q=1.6 x 10−19C) enters a crossed-field velocity selector with magnetic and electric fields of 2 mT and 6.000E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?
8. Example 11.9 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:kh61-j3_@2/116-The-Hall-Effect_1
The silver ribbon shown are a=3.5 cm, b=2 cm, and c= 0.2 cm. The current carries a current of 100 A and it lies in a uniform magnetic field of 1.5 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hall potential between the edges of the ribbon.
9. Example 11.10 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:AMMcl3_q@7/117-Applications-of-Magnetic-F_1 A cyclotron used to accelerate alpha particlesm=6.64 x 10−27kg, q=3.2 x 10−19C) has a radius of 0.5 m and a magneticfield of 1.8 T. What is their maximum kinetic energy?