Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 1.6, Problem 1.59P
To determine
The value of the integral of function
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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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- 1.1 Give a physical interpretation of what is meant by the curl of a vector. 1.2 Suppose a vector function A is given by A = -y i + x j and another vector function B is given by B = x j. Calculate (i) the curl of A: and (ii) the curl of B: 1.3 In which direction are the curls pointing? Hence what can you say about their divergence and why?arrow_forwardYour formula is correct, but number is not. You forgot to multiply t=24s in step 1, at the line .... = 999v. So follow your formula, the answer will be 77.34m. I rated (y).arrow_forwardProblem 1.45. As an illustration of why it matters which variables you hold fixec when taking partial derivatives, consider the following mathematical example. Le w = ry and z = yz. (a) Write w purely in terms of x and z, and then purely in terms of y and z. (b) Compute the partial derivatives and and show that they are not equal. (Hint: To compute (ðu/dz)y, use i formula for w in terms of r and y, not z. Similarly, compute (ðu/ar}: from a formula for w in terms of only z and z.)arrow_forward
- Problem 1.15 Calculate the divergence of the following vector functions: (a) va = x² + 3xz²ŷ - 2xz2.arrow_forwardStep 1 Rewrite the original integral Therefore, let du a² + u² (²) dt as + 16 = arctan(y) to Step 2 Use the following integration formula for the inverse trigonometric functions. 1.20 t (27²2² +42 (2) ot = (- t 1 + X X 4 2 (2) dt arctant arctan tan()+c 4 ✓)) + Carrow_forwardEvaluate the integral: 1 dx 2x2 —Зх — 2arrow_forward
- Evaluate the integral. dx (x – 4)(x – 3)(x + 5) | (Use symbolic notation and fractions where needed. Use C for the arbitrary constant.) dx %3D J (x – 4)(x – 3)(x + 5)arrow_forward(e) v,y &+(2xy+)9+2yz &. Problem 16 Sketch the vector function %3D and compute its divergence. The answer may surprise you...can you explain it?arrow_forwardintersecting cylinders defined by x + y2 6 to and x? + z? = a' is V= 16a/3. 1-36. Find the value of the integral fs A da, where A = xi - yj + zk and Sis the closed surface defined by the cylinder c x + y2. The top and bottom of the cylinder are at z = d and 0, respectively.arrow_forward
- 1.36 Expand log x in powers of (x – 1) by Taylor's series. -arrow_forward40 Q.14 The integral of the vector Ä(p, q, z) coso ô (standard notation for cylindrical coordinates is used) over the volume of a cylinder of height L and radius R, is: (A) 207R,L (î + j) (B) 0 (C) 40πR, Lj ( D) 40πR, L tarrow_forward1.3 Give the function f(x,y,z) = 3x2 – 2xyz +y² – 10z. Find- -at the point (2,1,1). дхду 1.4 Find a unit vector normal to the surface (x, y, z) = 2xz – x²y at the point (-3,4,5)arrow_forward
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