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Gauss’s Law (III)

Gauss’s Law (III). Examples.

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Gauss’s Law (III)

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  1. Gauss’s Law (III) • Examples

  2. Example 1: Consider a closed triangular box resting within a horizontal electric field of magnitude E = 7.80 × 104 N/C as shown below. Calculate the electric flux through:a) the vertical rectangular surfaceb) the slanted surfacec) the entire surface of the box.

  3. Solution

  4. Example 2: A cone with base radius R and height h is located on a horizontal table. A horizontal uniform field E penetrates the cone, as shown below. Determine the electric flux that enters the left-hand side of the cone.

  5. Solution Note:

  6. Example 3: A solid plastic sphere of radius 10.0 cm has charge with uniform density throughout its volume. The electric field 5.00 cm from the center is 86.0 kN/C radially inward. Find the magnitude of the electric field 15.0 cm from the center.

  7. Solution

  8. Example 5: A sphere of radius R surrounds a point charge Q , located at its center. a) Find the electric flux through a circular cap of half-angle θb) What is the flux for (i) θ = 90° and (ii) θ = 180°?

  9. Solution

  10. Example 4: An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as: where ρo, a, and b are positive constants and r is the distance from the axis of the cylinder. Use Gauss’s law to determine the magnitude of the electric field at radial distances:a) r < R b) r > R

  11. Solution

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