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In this lesson we look at finding the divergence of vector field in three different coordinate systems. The same vector field expressed in each of the coordinate systems is used in the examples. Related to this Question Prove or disprove that if \...
A vector field is given as follows: f = (x^2y + x y^2) i + (x^2y) j The divergence of this field evaluated at (x, y) = (2, 2) is ___. Calculate the circulation of the field F = 5yi + yj + zk where C is the counterclockwise-oriented ellipse \frac{x^2}{4} + \...
Calculate the divergence and the curl for the function: y2 = y^2j + zxk. Evaluate the following. A.\ \int_2^6 (3x^2 - 2x - 1)\Delta(x - 3) dx\\ B.\ \int_0^5 \cos x \Delta (3x) dx How can the universe be both infinite but expanding? How to find intervals in a s...
Faraday's law allows you to calculate the electromotive force in a loop of wire resulting from a changing magnetic field. A simple example is a loop of wire, with radius r = 20 cm, in a magnetic field that increases in magnitude from Bi= 1 T to Bf= 10 T ...