Answers to selected problems from Jackson's Classical by van Wijk K. PDF


By van Wijk K.

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Bracewell. The Fourier Transform and Its Applications. McGraw-Hill Book Company, first edition, 1965. J. Duffin. Electricity and Magnetism. McGraw-Hill Book Company, fourth edition, 1990. [3] ?.?. Griffith. Electricity and Magnetism. , third edition, 1999. D. Jackson. Classical Electrodynamics. , third edition, 1999.

SCATTERING AND DIFFRACTION B(x) = × 2ıE0 eıkr ka sin θ cos φ kb sin θ sin φ k×E = sin sin c 2 2 cπr sin2 θ cos φ sin φ 2 zˆ sin θ cos φ(sin(φ − β)) − sin θ sin φ(cos θ sin β) − x ˆ sin2 θ sin φ(sin(φ − β)) − cos θ cos θ cos β − yˆ sin2 θ cos φ(sin(φ − β)) − cos θ(cos θ sin β) × . 17) The power per unit angle is defined as dP dω = r2 |E|2 = 2Z0 2E02 sin2 Z0 k 2 π 2 sin θ cos2 φ sin2 φ sin2 θ sin2 (φ − β) + cos2 θ . 18) b. 19) where the assumption is that the scalar ψ(x ) in the aperture is the magnitude of the incoming field: ψ(x ) = E0 eık0 ·x = E0 eıkz .

There a four legs to the trip. We’ll do the calculations on the first and then use symmetry to find the total answer. The first leg is five years to the people in the rocket ship: t1 = 5 years. They experience an acceleration of a1 = g in the direction which I will call xˆ. What we want to know is 50 CHAPTER 11. SPECIAL THEORY OF RELATIVITY how long are those five years in the rocket ship to the observers (the other part of the twins) on earth. In other words, what is t? 15) 1 . 16) 1 − β2 The twin in the rocket ship feels a force but does not move in its reference frame: x = 0, so v c β= and γ= dt = γdt .

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Answers to selected problems from Jackson's Classical electrodynamics by van Wijk K.

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