Problem 5.6 (a) A phonograph record carries a uniform density of "static electricity" ?. If it rotates at angular velocity ?, what is the surface current density ? at a distance ? from the center? (b) A uniformly charged solid sphere, of radius ? and total charge ?, is centered at the origin and spinning at a constant angular velocity ? about the ? axis. Find the current density ? at any point (?, ?,?) within the sphere.
Problem 5.33 |Magnetostatics |Griffith |3rd ed.
Problem 5.33
Show that the magnetic field of a dipole can be written in coordinate-free form:? ⃗_??? (? ⃗ )=?_?/?? ?/?^? [?(? ⃗.? ̂ ) ? ̂\ −? ⃗ ]
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Capacitance of Two Parallel Wires
Question: Estimate the capacitance per unit length of two very long straight parallel wires, each of radius R, having uniform charge densities +λ and -λ, and separated by a distance d which is large compared to R (d≫R), as shown in Fig.
Approach: We have derived using Gauss’s law that the electric field outside a long wire is directed radially outward and has magnitude E ⃗=2kλ/r r ̂.
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Force on Dielectric Slab
Consider the system as shown in given figure.
We have always pretended that the field is uniform inside a PPC and zero outside. If this were literally true then there should be no force on dielectric at all.
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Problem 16 | Chapter 29 | Electric Field and Potential
Problem 16
Three equal charges, 2.0×10^(−6) ? each, are held fixed at the three corners of an equilateral triangle of side 5 ??. Find the Coulomb force experienced by one of the charges due to the rest two.
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