Classical Electromagnetic Theory (Fundamental Theories of by Jack Vanderlinde

By Jack Vanderlinde

This ebook claims to bridge the space among undergrad ebook and Jackson's. yet i don't locate it completed the aim. It comprises a few solid sections and that i use it in basic terms as a secondary e-book. I nonetheless need to use Jackson's as my basic resource. yet that's not to assert i admire Jackon's. I hate it like lots of people do, yet i don't discover a greater replacement. Electrodynmics is the single quarter that i have never came upon a superb grad point textual content ebook for self examine. i'm simply learning the low frequency half. My curiosity isn't really in waves. So, my reviews basically practice to that half.

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Extra info for Classical Electromagnetic Theory (Fundamental Theories of Physics)

Example text

6: Find the dipole moment of a sphere of radius a centered on the origin bearing charge density ρ = ρ0 z for r ≤ a. Solution: We exploit the convenient normalization of spherical harmonics (F–45) to simplify the integration. 4) Symmetry dictates that the remaining components vanish. Of course we could have integrated ρ0 z over the sphere directly to obtain the same results. 2 Interactions with the Field For electric monopoles we have already seen that the force on a charge is given by F = q E. 1, it should be clear that in a uniform field the force on one of the charges is exactly balanced by the opposite force on the second charge, leaving us with zero net force.

To be explicit we assume that the source coordinates r are consistently smaller than r (only then does the multipole expansion make sense), and we can write 1 r·r 1 1 = + 3 + 5 |r − r | r r 2r 3,3 xi xj 3xi xj − δij r 2 + . . (2–11) i=1 j=1 leading to V (r ) = 1 4πε0 ρ(r ) 3 d r |r − r | (2–12) 36 Classical Electromagnetic Theory = 1 4πε0 r· ρ(r )d3 r + r xi xj + = 1 4 πε0 q r·p + 3 + r r ρ(r )r d3 r r3 ρ(r ) 3xi xj − δij r 2r5 2 d3 r + ... (2–13) xi xj Qij + ... 2r5 (2–14) Here q is the total charge of the source, p= ρ(r )r d3 r (2–15) is the dipole moment of the distribution and Qij ≡ ρ(r )(3xi xj − δij r 2 )d3 r (2–16) is the ij component of the Cartesian (electric) quadrupole moment tensor.

2-9 Find the quadrupole moment of a rod of length L bearing charge density ρ = η (z 2 − L2 /12) , with z measured from the midpoint of the rod. 2-2 Find the dipole moment of a thin, 2-10 Show that the potential generated charged rod bearing charge density ρ = by a cylindrically symmetric quadrupole at the origin is λ z δ(x) δ(y) for z ∈ (−a, a). 2-3 Compute the curl of (2–23) to obtain (2–25). V = Qzz (3 cos2 θ − 1) 16πε0 r3 2-4 Show that the dipole moment of a 2-11 Find the charge Q contained in a charge distribution is unique when the sphere of radius a centered on the origin, whose charge density varies as ρ0 z 2 .

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