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Section 5: Electromagnetism II

1. Gauss's Law

A point charge of \(+2 \text{ C}\) is located at the origin. Calculate the electric flux through a spherical surface of radius \(1 \text{ m}\) centered at the origin.

2. Ampere's Law

Two long, parallel wires are \(10 \text{ cm}\) apart and carry currents of \(5 \text{ A}\) in opposite directions. Calculate the magnitude and direction of the magnetic field at a point midway between the wires.

3. Biot-Savart Law

A small segment of a line wire of length \(0.1 \text{ m}\) carries a current of \(3 \text{ A}\). The segment is located at a distance of \(0.2 \text{ m}\) from a point \(P\). Calculate the magnetic field at point \(P\) due to this current segment (assume the segment is perpendicular to the line connecting it to point \(P\)).

4. Magnetic Torque

A rectangular loop of wire with dimensions \(10 \text{ cm}\) by \(5 \text{ cm}\) carries a current of \(2 \text{ A}\). A uniform magnetic field of \(B = 0.3 \text{ T}\) is applied parallel to the plane of the loop. What is the magnitude of the magnetic torque on the loop?

5. Energy Stored by charge in a capacitor

We have parallel-plate capacitor with the following parameters:

  • \(S = 0.02\,\mathrm{m^2}\)
  • \(d = 5\,\mathrm{mm}\)

  • \(U = 500\,\mathrm{V}\)

  • Calculate the capacitance \(C\) of the capacitor.

  • Calculate the energy \(U\) stored in the capacitor.
  • Calculate the electric field intensity \(E\) between the plates.
  • Calculate the force of attraction \(F\) between the plates.

6. EM Wave Analysis

An electromagnetic wave has its electric field component described by \(E_y(x,t) = 100 \sin(10^7 x - \omega t) \text{ V/m}\). What is the direction of propagation? What is the wavelength \(\lambda\)? What is the angular frequency \(\omega\)? What is the equation for the magnetic field component?

7. Wavelength and Frequency

The human eye is most sensitive to light with a wavelength of about \(550 \text{ nm}\). What color does this correspond to in the visible spectrum? What is the frequency of this light?

8. EM Spectrum

List the following types of electromagnetic radiation in order of increasing wavelength: Infrared, Ultraviolet, Microwaves, X-rays, Radio waves, Gamma rays.

9. Refraction (Snell's Law)

A light ray travels from air (\(n=1.00\)) into glass (\(n=1.50\)). If the angle of incidence is \(30^\circ\), what is the angle of refraction?

10. Speed of Light in Media

What is the speed of light in a diamond, which has an index of refraction \(n = 2.42\)?