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- This problem is designed to give you practice using the Dirac delta function. Eval- uate the following integrals. Show your reasoning.Two infinite sheets of current flow parallel to the y-z plane as shown. The sheets are equally spaced from the origin by x = 6.1 cm. Each sheet consists of an infinite array of wires with a density n = 15 wires/cm. Each wire in the left sheet carries a current l₁ = 3.3 A in the negative z- direction. Each wire in the right sheet carries a current 1₂ = 4 A in the positive z-direction. R 1₁ H P % % OOOO OOO S XWhat is the square root of 1023? (Hints: 10 is an integer number. Integer numbers are exact, they don't have any uncertainty. The result however is going to be a real number. Computers approximate real numbers using floating point numbers. Floating point numbers have a given number of significant figures or digits. LON-CAPA typically expects 3, 4 or 5 digits. 2 or 1 is not enough, 6 or more is too many. Very large or very small numbers are expressed in scientific or exponential notation like the number above. Numbers in scientific notation are entered to computer software - like LON- CAPA as 1.23E15 or 1.23e15, for example; and 1.23E-15 or 1.23e-15, if the exponent is negative. If both the number and the exponent are negative, then you type -1.23E- 15 or -1.23e-15. On calculators the button is usually labelled as 'EE', but 'E' or 'EEX' or 'Exp' are also possible.)
- I need help with number 3(3) The natural independent variables for U are (S, V), from dU = TdS – pdV. U = U(S,V) (), instead. Show that U = U (V,T) leads to a much more complicated expression for p, namely gives simple expressions for T and p as T = and ().: Suppose you use (V,T) p = - V dT + f(V), %D T where f (V) is an unknown function of V.This problem is designed to give you practice using the Dirac delta function. Eval- uate the following integrals. Show your reasoning.