introduction to electrodynamics,griffith-3ed

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Undergraduate electrodynamics text

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Simple addition and subtraction are like you will do for scalars
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The magnitude of the vector squared
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also A^2 + 2ABCostheta +B^2 When C is A + B
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Same as the dot product
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unlike the dot product , the cross product is not commutative
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area of a parallelogram is base times altitude
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A vector A can be represented in the Cartesian coordinate as the sum of the components in the direction of each unit vector times the unit vector
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B+C=ASo C= A-B
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Cartesian coordinate with unit vectors
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A vector A and its components on the Cartesian coordinate
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Magnitude of A
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If a line was drop on top the cube, and equilateral triangle of sides square root of 2 will formed. The angle is then 60 degrees because we know that angle in an equilateral is 60 degrees.
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A vector perpendicular to the plane containing a vector is the cross product. Because the cross product produces another vector perpendicular to the plane of the two original vectors. A unit vector is just that new vector (cross product) divided by the magnitude of the two original vectors. See pg 22 of analytical mechanics for example
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The Bac Cab rule
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This is esentially dr
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SEPERATION VECTOR IS EQUAL TO THE FIELD POINT MINUS THE SOURCE POINT
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THESE ARE FOR THE SEPERATION VECTOR
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SKIPPED THIS SECTION
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SMALL DERIVATIVE
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LARGE DERIVATIVE
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THE GRADIENT OF THE MAGNITUDE OF THE POSITION VECTOR IS THE UNIT VECTOR POINTING IN THE RADIAL DIRECTION
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THE DEL OPERATOR WHICH WITH A SCALAR IS THE GRADIENT
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THE DEL OPERATOR DOTTED ON A VECTOR IS THE DIVERGENCE
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THE DEL OPERATOR CROSSED WITH A VECTOR IS A CURL
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LAPLACIAN OF V GOTTEN FROM THE DIVERGENCE OF A GRADIENT
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General solution for the potential
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POTENTIAL INSIDE
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POTENTIAL OUTSIDE
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GENERAL FORM TO DETERMINE COEFFICIENTS
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COEFFICIENT FOR A
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COEFFICIENT FOR A
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