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(8%) Problem 7: A wire of circular cross-section carries current density that is not uniform but varies with distance from the center as j(r)=A(1-r/R), for radius r in the range 0 < r < R. Here, A is a constant with units amperes per square meter, and the radius of the wire is R = 0.33 mm. 11% Part (a) Find an expression for the current enclosed in a cylinder with a radius of r < R. i(r) = 2 ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? A ( ( r^2 / 2 ) - ( r^3 / ( 3 R ) ) ) 11% Part (b) If the total current in the wire is I, find an expression for the constant A, in terms of the other variables in the problem. A = ( 3 I ) / ( ? R^2 ) 11% Part (c) If the total current is 4.5 A, what is the constant A, in amperes per square meter? A = 39459903.24 A = 3.946E+7 11% Part (d) Find an expression for the magnetic field inside the wire, r < R, in terms of the current I. B(r) = ( ( 3 ?? I ) / ( ? R^2 ) ) ( ( r / 2 ) - ( r^2 / ( 3 r ) ) ) 11% Part (e) Find an expression for the magnetic field outside of the wire, for r > R. B(r) = ( ?? I ) / ( 2 ? r ) 11% Part (f) For what r, in meters, is the current enclosed maximum? r?,I = 0.33 * 10^( - 3 ) r?,I = 0.00033 11% Part (g) What is the maximum value of the enclosed current, in amperes? i_max = 4.5 11% Part (h) For what r, in meters, is the magnetic field maximized? r?,B = 0.2475 * 10^( - 3 ) r?,B = 2.475E-4 11% Part (i) What is the maximum value of the magnetic field, in tesla?

          (8%) Problem 7: A wire of circular cross-section carries current density that is not uniform but varies with distance from the center as
j(r)=A(1-r/R),
for radius r in the range 0 < r < R. Here, A is a constant with units amperes per square meter, and the radius of the wire is R = 0.33 mm.

11% Part (a) Find an expression for the current enclosed in a cylinder with a radius of r < R.
i(r) = 2 ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? A ( ( r^2 / 2 ) - ( r^3 / ( 3 R ) ) )

11% Part (b) If the total current in the wire is I, find an expression for the constant A, in terms of the other variables in the problem.
A = ( 3 I ) / ( ? R^2 )

11% Part (c) If the total current is 4.5 A, what is the constant A, in amperes per square meter?
A = 39459903.24
A = 3.946E+7

11% Part (d) Find an expression for the magnetic field inside the wire, r < R, in terms of the current I.
B(r) = ( ( 3 ?? I ) / ( ? R^2 ) ) ( ( r / 2 ) - ( r^2 / ( 3 r ) ) )

11% Part (e) Find an expression for the magnetic field outside of the wire, for r > R.
B(r) = ( ?? I ) / ( 2 ? r )

11% Part (f) For what r, in meters, is the current enclosed maximum?
r?,I = 0.33 * 10^( - 3 )
r?,I = 0.00033

11% Part (g) What is the maximum value of the enclosed current, in amperes?
i_max = 4.5

11% Part (h) For what r, in meters, is the magnetic field maximized?
r?,B = 0.2475 * 10^( - 3 )
r?,B = 2.475E-4

11% Part (i) What is the maximum value of the magnetic field, in tesla?

(8%) Problem 7: A wire of circular cross-section carries current density that is not uniform but varies with distance from the center as
j(r)=A(1-r/R),
for radius r in the range 0 < r < R. Here, A is a constant with units amperes per square meter, and the radius of the wire is R = 0.33 mm.

11% Part (a) Find an expression for the current enclosed in a cylinder with a radius of r < R.
i(r) = 2 ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? A ( ( r^2 / 2 ) - ( r^3 / ( 3 R ) ) )

11% Part (b) If the total current in the wire is I, find an expression for the constant A, in terms of the other variables in the problem.
A = ( 3 I ) / ( ? R^2 )

11% Part (c) If the total current is 4.5 A, what is the constant A, in amperes per square meter?
A = 39459903.24
A = 3.946E+7

11% Part (d) Find an expression for the magnetic field inside the wire, r < R, in terms of the current I.
B(r) = ( ( 3 ?? I ) / ( ? R^2 ) ) ( ( r / 2 ) - ( r^2 / ( 3 r ) ) )

11% Part (e) Find an expression for the magnetic field outside of the wire, for r > R.
B(r) = ( ?? I ) / ( 2 ? r )

11% Part (f) For what r, in meters, is the current enclosed maximum?
r?,I = 0.33 * 10^( - 3 )
r?,I = 0.00033

11% Part (g) What is the maximum value of the enclosed current, in amperes?
imax = 4.5

11% Part (h) For what r, in meters, is the magnetic field maximized?
r?,B = 0.2475 * 10^( - 3 )
r?,B = 2.475E-4

11% Part (i) What is the maximum value of the magnetic field, in tesla?

Added by -Ngeles B.

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