# Electromagnetics 2

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1.5 Vector Field Vector field is defined as a vector function of a position vector. 1.6 The Dot product  The dot product or scalar product is defined as the product of the magnitude of A, the magnitude of B and the cosine of the smaller angle between them, | || |  The dot, or scalar, product is a scalar and it obeys the commutative law  Given of A and B is and the dot product because    | | , any vector dotted with itself is unity | || | | | , component vector of B in the direction of a. Example 1.6 Follow the link: https://youtu.be/vrFqUOb_cTE Follow the links below for further information: https://www.youtube.com/watch?v=0iNrGpwZwog 1.7 The Cross Product  The cross product is a vector, the magnitude of is equal to the product of the magnitudes of A, B and the sine of the smaller angle between A and B; the direction of is perpendicular to the plane containing A and B and is along that one of the two possible direction perpendiculars which is in the direction of advanced of a right-handed screw as A is turned into B. | || |  Given A and B is But, and , , and Or written in determinant form, and the cross product of and it follows , | Follow the links below for further information: https://www.youtube.com/watch?v=gPnWm-IXoAY 1.8 Circular Cylindrical Coordinate System | The relationship between the Cartesian variables x, y, z and the cylindrical coordinate variables ρ, φ, z. There is no change in the variable z between ...
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