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37 Cards in this Set
- Front
- Back
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Biot-Savart Law Equation |
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unit vector r |
(r in the vector form)/(absolute value of r) |
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Cross Product |
|A (vector form) x B (vector form)|=|A||B| sin theta |
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Right Hand Cross Product Rule |
The direction of the cross product may be found by application of the right hand rule as follows: Using your right hand,Point your index finger in the direction of the first vector A.Point your middle finger in the direction of the second vector B.Your thumb will point in the direction of the cross product C. |
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Magnetic Field at the Center of a Coil |
B=(μ0*I)/(2*r)
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Line of Integral- Parallel with the Field |
BL |
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Line of Integral- Perpendicular with the Field |
0 |
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Line of Integral- Some angle with the Field |
BLcosθ |
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Ampere's Law |
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Dot Product |
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Volume of Box with width a, depth b, and height c |
abc |
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Area of Box with width a, depth b, and height c |
2(ab+bc+ac) |
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Volume of Sphere with radius R |
(4/3)πR^3 |
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Area of Sphere with radius R |
4πR^2 |
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Volume of Hollow Spherical Shell with Outer Radius b and Inner Radius a |
(4/3)π(b^3-a^3) |
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Area of Hollow Spherical Shell with Outer Radius b and Inner Radius a |
4πb^2 |
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Volume of Cylinder with Radius R and Length L |
πR^2L |
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Area of the End of the Cylinder with Radius R and Length L |
πR^2 |
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Area of the Side of the Cylinder with Radius R and Length L |
2πRL |
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Volume of a Hollow Cylindrical Shell of Length L, with Outer Radius b and Inner Radius a |
πL(b^2-a^2) |
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Area of the Ends of a Hollow Cylindrical Shell of Length L, with Outer Radius b and Inner Radius a |
π(b^2-a^2) |
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Area of the Outer Surface of a Hollow Cylindrical Shell of Length L, with Outer Radius b and Inner Radius a |
2πbL |
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Area of the Inner Surface of a Hollow Cylindrical Shell of Length L, with Outer Radius b and Inner Radius a |
2πaL |
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Steps for using Ampere's Law to determine the magnetic field |
1. Draw the path of integration you would like to use to calculate the path of integral ∲B●dl. 2. Draw and label B and dl vectors. 3.Derive an expression for ∲B●dl. 4. Derive an expression for the current enclosed by your integration path. 5. Use Ampere's Law to derive an expression for the magnitude of the magnetic field. |
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Magnetic Field Outside of a Solenoid |
0 |
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Magnetic Force on a Single Charge |
Magnetic Field= q*V*B*sinθ |
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Magnetic Force on a Current |
Magnetic Field= I*L*B*sinθ |
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A is proportional to B |
A=KB |
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A is inversely proportional to B |
A=K/B |
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Faraday's Law |
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Ampere's Law |
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The equation for the statement: "A is proportional to B" |
A=kB |
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The equation for the statement: "A is inversely proportional to B" |
A=k/B |
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Is it possible for a magnetic field to cause a charge to slow down or speed up? |
No, it is only possible for the magnetic field to make the charge to move at a constant speed. |
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The mathematical relationship between the electric field and the magnetic field |
-E=vB |
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Lenz's Law |
If an induced current flows, its direction is always such that it will oppose the charge which produced it. |
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Steps for Faraday's/Lenz's Law Problem |
1. Draw a picture 2. Find the magnetic field 3. Decide if the shape is moving closer to, away from, or not moving at all from the magnetic field. 4. Figure out the induced magnetic field. 5. Using the RHR to find the direction of the current around the shape. 6. Write the expression for the flux a. Find B b. Find dA, a slice of the width w/ the same length, dA is perpendicular to the shape form either side. c. Find θ, when dA is parallel w/ B θ=0, when dA is perpendicular w/ B θ=180 7. Write the limits of integration 8. Simplify the integral 9. Find emf, using dϕ/dt, decide the variable of the equation 10. Find the derivative 11. Simplify the derivative 12. Find I using the equation I=emf/R |
