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Chapter Review

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**The behavior of bar magnets**

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**Our Earth itself has a magnetic field**

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**Charges moving with respect to a field**

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**Charges moving with respect to a field**

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**Charges moving with respect to a field**

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The Right Hand Rule Using the right hand rule, one may determine the direction of the field produced by a moving positive charge.

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**Magnetism and circular motion**

F = |q|vB If the motion is Circular F = mv2/R R = mv/ |q|B ω = v/R = |q|B/m

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**Force on a conductor with current**

F = ILB

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**Applications of force on a conductor**

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**Magnetic field of long straight conductor**

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**B = μ0I/(2πr) Magnetic field of a long, straight wire:**

r is the distance from the wire μ0 is called the permeability of vacuum μ0 = 4π x 10-7 T.m/A

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**Fields in two conductors side-by-side**

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**Fields in two conductors side-by-side**

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**F = μ0 L(I1 I2)/(2πr) F/L = μ0 (I1 I2)/(2πr)**

2 wires with currents flowing in the same direction attract each other 2 wires with currents flowing in opposite directions repel each other F = μ0 L(I1 I2)/(2πr) Force per unit length F/L = μ0 (I1 I2)/(2πr)

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**Magnetic field at the center of a circular loop B = μoI /(2R) **

Currents in a loop Magnetic field at the center of a circular loop B = μoI /(2R) For N loops: B = μo NI /(2R)

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**Electromagnetic Induction**

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**Does the field induce a current or not?**

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**Magnetic flux at various orientations**

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**Magnetic flux at various orientations**

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**Magnetic flux at various orientations**

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**If we have a coil with N identical turns, then**

FRADAY’s LAW When the magnetic flux ΦB changes in time, there is a an induced emf directly proportional to the time rate of change of the magnetic flux : ɛ = |Δ ΦB /Δt | If we have a coil with N identical turns, then ɛ = N |Δ ΦB /Δt |

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Vab = vBL a b

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Lenz’s Law

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Lenz’s Law

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Transformers

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**If energy completely transformed**

TRANSFORMERS V2 / V1 = N2 / N1 If energy completely transformed V1I1 = V2I2

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**Energy associated with an induced current.**

energy is stored in an electronic device.

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The R-L circuit

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The L-C circuit

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**In the case of an inductor with a capacitor,**

the energy is transferred from the electric field (capacitor) to magnetic field (inductor) and vice versa. The total energy is however conserved: The back and forth of the energy constitutes an oscillatory behavior with a frequency ω:

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A metal loop moves at constant velocity toward a long wire carrying a steady current , as shown in the figure . The current induced in the loop is directed A) Clockwise B) counterclockwise C) zero

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**B out of page increasing ΔΦ out of page Bi into page**

A metal loop moves at constant velocity toward a long wire carrying a steady current , as shown in the figure . The current induced in the loop is directed A) Clockwise B) counterclockwise C) zero B out of page increasing ΔΦ out of page Bi into page

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The slide wire of the variable resistor in the figure is moved steadily to the right, increasing the resistance in the circuit. While this is being done, the current induced in the small circuit A is directed : A) clockwise B) counterclockwise C) zero

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**I A) clockwise B) counterclockwise C) zero**

I=V/R I decreases when R increases B due to I decreases as I decreases B out of page and decreases hence ΔΦ into page Bi out of page I

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