Suppose we have an infinite line of charge such that the linear charge distri- bution is given by A(x) = where a is a constant with dimension of length. We can determine the electrostatic potential some perpendicular distance z above the line to be (in SI units) -2² /a² e 2Q V(2) = 4megaz o VI+/dz , VI+ x²/z²" and of course we would like to evaluate the integral. (a) (paper) Make the change of variables x = aq, so that you get e-q? 2Q V (2) = (1) VI+ a²q²/z²° and then with y = z/(/2a), show that this can be written as V(2) = -ev² Ko(y³) , 4t€0a where Ko is a modifed Bessel function. Do this by looking up integral forms of the Bessel function and compare them to Eg. (1).

Q: X = acos'0 , y = b sin°0 %3D

A:

Q: 5. In rectangular coordinates verify that V · V x A = 0 where A = xyz(ê+ ŷ + 2) by carrying out the…

A:

Q: 1 y = V5 + cos I

A: We have to find dydx of the given function: y=15+cos x4 We know the formula of derivatives,…

Q: That question please

A:

Q: 5. Find the following derivatives: a) y = x?e-2/x b) y = t tan -t- t -Int

A: Given:  5)a) y=x2e-2xb) y=ttan-1t-12lnt To find: Derivatives of the given functon.

Q: (sin(æ) + 2 cos(y)) dy ^ dz + (zổ – y cos(x)) dz A dæ + 11xyz dx ^ dy. Find dw. dw dx ^ dy ^ dz

A:

Q: Find y' and y". y = cos(sin(90)) y' %3D %3D

A: We have to find

Q: If  sin⁡x=e^y,  0<x<π, what is dydx in terms of  x?

A: Given sin x = ey   ..................(1) Differentiating both sides with respect to x  d(sinx) / dx…

Q: dz Different iate implicit ly to find and if z'yz + In(ry) + sin(yz) = 10. ду

A:

Q: - y= arctan yx h. y= sin(arccos x)

A: