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**Text Reading**: Giancoli, *Physics - Principles with Applications*, Chapter 20: 5 to 12

*20.5: Magnetic fields*. As with electrical fields and gravitational fields, the strength of the magnetic field generated by current a wire depends on the amount of current**due**to current in wires*i*and the distance from the wire. Note that since we don't have a point source, but a linear source, field strength varies inversely as distance, not as the square of the distance: B ∝ i/r. The constant of proportionality depends on the medium through which the magnetic field acts. In "free space", this value is given by the permeability constant μ_{0}(do not confuse this with the FRICTION constant used in analysis of forces!).*20.6: Magnetic forces on parallel wires*. If we put two wires parallel to each other at a distance r, each generates a magnetic field that influences the current in the other wire. (Now you know why you get interference when you have two electrical devices too close together). We can calculate the field**B**of each wire on the other wire by looking at the distance*r*(or d if you prefer), and the current i_{1}and i_{2}in each wire,*and the direction of the current in the wires*. The latter is important in determining the direction of the net force on the wires: remember that this force**F**will be at right angles (using the right hand rule) to the field lines of the magnetic fields generated by the current.*20.7: Solenoids and Electromagnets*. A**solenoid**is simply a looped current-carrying wire that can act like a magnet. An**electromagnetic**is a magnetizable object (like a piece of iron) which becomes magnetized when placed inside the looped wires of a solenoid: as it becomes magnetized, it increases the net magnetic field. Solenoids (where low magnetic fields are required) and electromagnets (where intense magnetic fields are required) are useful for creating magnetic fields that can be instantly turned on and off. They are used in switches and locks.*20.8: Ampere's law*. Ampere's law looks at the general case of magnetic fields arising from current traveling through any wire (not just straight wires in parallel situations). It states that the total of the magnetic field B acting through a virtual "loop" of any shape (as long as it lies in a plane -- could be a circle, a square, or a squiggly jiggle) around a current-bearing source is equal to the total current enclosed by the loop, as modified by the medium involved. If we are in "free space" (air is close enough), then we can use the permeability constant as our constant of proportionality. We add up all the little bits of our loop-of-any-shape Δl times the**B**field pointing along each individual bit, we can determine the enclosed current*i*.You can now see where the circumference distances comes from in the previous sections: since B

_{||}is the same for each point on a circle around a current-bearing wire, and the sum of the increments of length around a circle is the circumference, we have $$\sum {B}_{\left|\right|}\text{}\Delta l\text{}=(2\pi r)\text{}B\text{}=\text{}{\mu}_{0}I$$*20. 9: Torques on current in loops*. If we place a current-bearing loop of wire in a magnetic field, the field will cause the loop to turn: this is how motors work. The torque (since it is rotating) on the loop is proportional to the current*i*passing through the loop, the strength of the magnetic field**B**, and the area A through which the field passes at a perpendicular angle. [Note that the*shape*of the loop is irrelevant: we are concerned only with the enclosed area.] The maximum magnitude of the torque (when the loop area is perpendicular to**B**is given by $$\tau \text{}=\text{}\mathrm{IAB}$$If we have lots of identical loops (as in a solenoid), then the torque is also proportional to the number N of loops: $$\tau \text{}=\text{}\mathrm{NIAB}$$

As the loop turns, of course, the Area changes as the sin of the angle between it and

**B**, so the general case is given by a cross-product rule: $$\tau \text{}=\text{}\mathrm{IAB}\text{}\mathrm{sin}\text{}\theta $$When the loop is parallal to the field, it presents no area to the field and no net torque acts on it.

In some sources, you may see the quantity NIA called the

*magnetic dipole moment*, and the equation then takes the form $$\tau \text{}=\text{}\mathrm{MB}\text{}\mathrm{sin}\text{}\theta $$*20.10-12: Applications - Galvanometers, Motors, Mass Spectrometers, Ferromagnetism*. Enjoy these sections; they are for your cultural enrichment!

- Magnetic field strength near a current-carrying straight wire: $$B\text{}=\text{}\frac{{\mu}_{0}}{2\pi}\text{}\frac{l}{r}\text{}=\text{}{\mu}_{0}\frac{I}{2\pi r}\text{}$$
- Force between two current carrying wires: $$F\text{}=\text{}{\mu}_{0}\frac{{I}_{1}{I}_{2}}{2\pi d}$$
- AmpĂ¨re's law: $$\sum {B}_{\left|\right|}\text{}\Delta l\text{}=\text{}{\mu}_{0}I$$

Magnetic field strength near a straight wire | B = μ_{0}I/2πr | μ_{0} is the permeability constant, which determines how magnetic force is propagated through a medium. The "0" indicates this is the propagation constant for a vacuum or "free space", which has the value 4 π * 10^{-7} T•m/A^{2}. Steel has a permeability about 100 times that of a vacuum, making it a good "magnetic conductor". |

Force on paralle conductors | F = μ_{0} I_{1}I_{2} l / 2 π d | This gives the force on a length l of wire #2 due to current I_{1} in wire 1 and I_{2} in wire two, when the wires are a distance d apart. |

Magnetic field of solenoid | B = μ_{0} IN/l | This gives the strength of the magnetic field generated by current I running through N loops of a wire within a given distance l |

Ampère's Law | Σ B_{||} Δ l = μ_{0} I_{enc} | The general rule for any closed path of segments Δl enclosing a medium carrying carrying current I_{enc}. This rule allows us to consider situations other than the field near a straight wire. |

**Read the following weblecture before chat**: Ampere's Law and Electromagnets

Use the physics simulation for a Charged Particle in a Magnetic Field — 3D.

- Play the simulation using default values. What happes to the charged particle as it makes at least three loops in the field?
- Adjust the mass of the particle to a new value and view the result from above and in 3D.
- Adjust the particle charge and view the result.
- Adjust the initial velocity in the x direction.
- Adjust the initial velocity in the y direction.

Interactive Physics Simulations are provided at the GeoGebra site GeoGebra site.

**Forum question**: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer**before**chat starts for this session.**Mastery Exercise**: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

**Required**: Complete the Mastery exercise with a passing score of 85% or better.- Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

If you want lab credit for this course, you must complete at least 12 labs (honors course) or 18 labs (AP students). One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!

**Lab Instructions**: The Magnetic field of a Solenoid

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