(9%) Problem 10: An electric current is flowing through a long cylindrical condu

Question

(9%) Problem 10: An electric current is flowing through a long cylindrical conductor with radius a = 0.35 m. The current density J = 7.5 A/m2 is uniform in the cylinder. In this problem we consider an imaginary cylinder with radius r around the axis AB ©theexpertta.com 13% Pa 13% Part(b) Express the magnitude of the magnetic field B at r in terms of the current through the imaginary cylinder 1 and its radius r nt inside the imaginary cvlindc rms /S 13% Part (c) Express B in terms of J and r. 13% Part (f) Express the magnitude of the magnetic field, B, at r> a in terms of 1 and r. 13% Part (h) For= 2 a, calculate the numerical value of B in Tesla 13% Part (d) For r = 0.5 a, calculate the numerical value of B in Tesla 13% Part (e) When r is greater than a, express the current inside the imaginary cylinder in terms of r, a and J 13% Part (g) Express B in terms of J, a and r Grade Summar Deductions Potential 0% 100% Submissions tan() | | ( 789 HOME sin cosO

Explanation / Answer

10. given current density J = 7.5 A/m^2 ( uniform in the cylinder)

radius a = 0.35 m

a. for r < a

current density = J ( as the current density is uniform )

b. current through the radius r cylinder , I = J*pi*r^2

consder another smaller cylinder insider radius r of radius b

consider a concentric shell at radius b of thickness db

then current through this shell = i = J*2*pi*b*db

magnetic field at r due to this current = 2ki/r = 2kJ*2*pi*b*db/r

total magnetic field = interate dB form b = 0 to b = r

B = 2kJ*pi*r

but J = I/pi*r^2

hence

B = 2kI*pi*r/pi*r^2 = 2kI/r ( where k is 10^-7)

c. B = 2kJ*pi*r

d. r = 0.5a

B = 2*10^-7*7.5*pi*0.5*0.35 = 8.2466*10^-7 T

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