Electromagnetism: Curl and Divergence

The divergence and curl mathematical operators are used to develop theorems of multivariable calculus and can be applied to physical topics such as fluids, electromagnetism, and elasticity theory. In our Physics 201 Electromagnetism class we learned multiple equations which use these operators. In this assignment we explore the connections between math and physics. Our poster displays a few applications of the divergence and curl operators in electromagnetism and shows how electric and magnetic fields are manifestations of the electromagnetic field. We include equations from our physics textbook “Six Ideas that Shaped Physics: Unit E” and plots made using Mathematica.

As shown in the equations, the divergence (or outwardness) of a field is found using the dot product. The divergence of a electric field is determined by its distribution. The divergence of a magnetic field is zero. On the right, we show that the curl (related to torque and twistedness) of a magnetic field is determined also by its distribution. Our closing point is that the electric and magnetic fields can be unified through Faraday’s Law and the extension of Ampere’s Law that a change in the magnetic field creates an electric field and visa versa.

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