(10%) Problem 6: An electric current is flowing through a long cylindrical conductor with radius a...

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(10%) Problem 6: An electric current is flowing through a long cylindrical conductor with radius a = 0.15 m. The current density J = 6.5 A/m² is uniform in the cylinder. In this problem we consider an imaginary cylinder with radius r around the axis AB. ¡A + a 1111 'B J Oth Part (a) When r is less than a, express the current inside the imaginary cylinder I, in terms of r and J. Part (b) Express the magnitude of the magnetic field B at r in terms of the current through the imaginary cylinder I, and its radius r. Part (c) Express B in terms of J and r. Part (d) For r=0.5 a, calculate the numerical value of B in Tesla. Part (e) When r is greater than a, express the current inside the imaginary cylinder in terms of r, a and J. Part (f) Express the magnitude of the magnetic field, B, at r> a in terms of I and r. Part (g) Express B in terms of J, a and r. Part (h) For r = 2 a, calculate the numerical value of B in Tesla. (10%) Problem 6: An electric current is flowing through a long cylindrical conductor with radius a = 0.15 m. The current density J = 6.5 A/m² is uniform in the cylinder. In this problem we consider an imaginary cylinder with radius r around the axis AB. ¡A + a 1111 'B J Oth Part (a) When r is less than a, express the current inside the imaginary cylinder I, in terms of r and J. Part (b) Express the magnitude of the magnetic field B at r in terms of the current through the imaginary cylinder I, and its radius r. Part (c) Express B in terms of J and r. Part (d) For r=0.5 a, calculate the numerical value of B in Tesla. Part (e) When r is greater than a, express the current inside the imaginary cylinder in terms of r, a and J. Part (f) Express the magnitude of the magnetic field, B, at r> a in terms of I and r. Part (g) Express B in terms of J, a and r. Part (h) For r = 2 a, calculate the numerical value of B in Tesla.