Introduction to Electrodynamics
4th Edition
ISBN: 9780321856562
Author: David J. Griffiths
Publisher: Addison-Wesley
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Chapter 1.1, Problem 1.7P
To determine
The magnitude of the separation vector and unit vector along the separation between source and field point.
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Chapter 1 Solutions
Introduction to Electrodynamics
Ch. 1.1 - Using the definitions in Eqs. 1.1 and 1.4, and...Ch. 1.1 - Prob. 1.2PCh. 1.1 - Prob. 1.3PCh. 1.1 - Prob. 1.4PCh. 1.1 - Prob. 1.5PCh. 1.1 - Prob. 1.6PCh. 1.1 - Prob. 1.7PCh. 1.1 - Prob. 1.8PCh. 1.1 - Prob. 1.9PCh. 1.1 - Prob. 1.10P
Ch. 1.2 - Prob. 1.11PCh. 1.2 - The height of a certain hill (in feet) is given by...Ch. 1.2 - Prob. 1.13PCh. 1.2 - Prob. 1.14PCh. 1.2 - Prob. 1.15PCh. 1.2 - Prob. 1.16PCh. 1.2 - Prob. 1.17PCh. 1.2 - Prob. 1.18PCh. 1.2 - Prob. 1.19PCh. 1.2 - Prob. 1.20PCh. 1.2 - Prob. 1.21PCh. 1.2 - Prob. 1.22PCh. 1.2 - Prob. 1.23PCh. 1.2 - Prob. 1.24PCh. 1.2 - Prob. 1.25PCh. 1.2 - Prob. 1.26PCh. 1.2 - Prob. 1.27PCh. 1.2 - Prob. 1.28PCh. 1.3 - Prob. 1.29PCh. 1.3 - Prob. 1.30PCh. 1.3 - Prob. 1.31PCh. 1.3 - Prob. 1.32PCh. 1.3 - Prob. 1.33PCh. 1.3 - Prob. 1.34PCh. 1.3 - Prob. 1.35PCh. 1.3 - Prob. 1.36PCh. 1.4 - Prob. 1.37PCh. 1.4 - Express the unit vectors in terms of (that is,...Ch. 1.4 - Prob. 1.39PCh. 1.4 - Prob. 1.40PCh. 1.4 - Prob. 1.41PCh. 1.4 - Prob. 1.42PCh. 1.4 - Prob. 1.43PCh. 1.5 - Evaluate the following integrals:
(a)
(b)
(c)...Ch. 1.5 - Prob. 1.45PCh. 1.5 - (a) Show that .
[Hint: Use integration by...Ch. 1.5 - Prob. 1.47PCh. 1.5 - Prob. 1.48PCh. 1.5 - Prob. 1.49PCh. 1.6 - (a) Let and . Calculate the divergence and curl...Ch. 1.6 - Prob. 1.51PCh. 1.6 - Prob. 1.52PCh. 1.6 - Prob. 1.53PCh. 1.6 - Prob. 1.54PCh. 1.6 - Prob. 1.55PCh. 1.6 - Prob. 1.56PCh. 1.6 - Prob. 1.57PCh. 1.6 - Prob. 1.58PCh. 1.6 - Prob. 1.59PCh. 1.6 - Prob. 1.60PCh. 1.6 - Prob. 1.61PCh. 1.6 - Prob. 1.62PCh. 1.6 - Prob. 1.63PCh. 1.6 - Prob. 1.64P
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- The vector field G is described by the vector function shown below. Evaluate G at point P(-3, 4, 5) G= yza x + xa y + x²/sqrt x² + y² azarrow_forwardGet the expression for the divergent of a vector field in spherical coordinates.arrow_forward7. a) Find the divergence of the vector field G(x, y, z)= ext+ln(xy) j+exyz k at (0, 2, -31 b) Find the curl of the vector field V(x, y, z)=(xyz)i + (3x²y)j + (xz² - y²z) k at (2,-1,1).arrow_forward
- Express the vector field W = (x² – y²)a, + xza, in the (a) Cylinderical coordinate at P(p = 6, q = 60, z = -4). (b) Spherical coordinate at P(r = 4, 0 = 30, p = 120). %3Darrow_forwardVerify if the following vector fields are conservative: a) Ã = ( ) 2y 1+2²+y: 1+z²+y? b) Ã, = (2ry – 2², 2yz + x², y² – 2xz) In case they are conservative, find their respective potential fields.arrow_forwardCan you show me an example of polar coordinates? (I am an engineering student, I would like to see an example answered)arrow_forward
- Q2: Express the vector field W = (x² – y²)ay + xza, in the (a) Cylinderical coordinate at P(p = 6, 9 = 60, z = -4). (b) Spherical coordinate at P(r = 4, 0 = 30, p = 120).arrow_forwardVerify if the following vector fields are conservative: a) A1 = (2x / 1+x^2+y^2 , 2y / 1+x^2+y^2) b) A2 = (2xy − z^2 , 2yz + x^2 , y^2 − 2xz) In case they are conservative, find their respective potential fields.arrow_forwardVerify if the following vector fields are conservative: a) Ã₁ = (2+ ₁ - ² - ³ ) 7 b) A₂ = (xy, yz, zx) c) A3 = (xxe*, -y, e²) In case they are conservative, find their respective potential fields.arrow_forward
- For the vector field ?(x,y,z) = < x+(y/z), sqrt(x^2+y^2), lnz > a) Find curl F b) Find div F c) State whether or not the vector field is conservative, and why.arrow_forwardSuppose the vector field F takes the values shown in the table below. Sketch this vector field on a piece of paper and find a formula for it. F Values of F y = 2 (-10, –10) (–10,–5) (-10,0) (-10, 5) (-10, 10) y = 1 (-5, –10) (-5, -5) {-5,0) | (-5, 5) (-5, 10) y = 0 (0, –10) (0, –5) (0,0) (0, 5) (0, 10) y = -1 (5, –10) (5, –5) (5, 0) (5,5) (5, 10) y = -2 (10, – 10) (10, –5) (10, 0) (10,5) (10, 10) x = -2 x = -1 x = 0 x = 1 x = 2arrow_forwardThe uniform vector field A = ay can also be expressed as?arrow_forward
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