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(a) (10 marks] A straight wire along the ź direction with a circular cross-section of radius...
A very long, straight conductor located along the z axis has a circular cross section of radius 10 cm
5-15 Exercises: 5.16. A very long, straight conductor located along the z axis has a circular cross section of radius 10 cm. The conductor carries 100 A in the z direction which is uniformly distributed over its cross section. Find the magnetic field intensity (a) inside the conductor and (b) outside the conductor. Sketch the magnetic field intensity as a function of the distance from the center of the conductor. 5-15 Exercises: 5.18. A fine wire wound in the form of...
A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose...
A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is J⃗ . The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship J⃗ =2I0πa2[1−(ra)2]k^forr≤a=0forr≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and I0 is a constant having units of amperes. A)Using Ampere's law, derive an expression for the magnitude of the magnetic field...
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor. (b) Det...
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor. (b) Determine the vector magnetic potential (A) both inside and outside the conductor from the relationship B V x A
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor....
b inside a current carrying wire A steady current I flows through a wire of radius...
b inside a current carrying wire
A steady current I flows through a wire of radius a. The current density in a wire varies with ras ) = kr2, where k is a constant and r is the distance from the axis of the wire. Find expressions for the magnitudes of the magnetic field inside and outside the wire as a function of r. (Hint: Find the current through an Ampèrian loop of radius r using thru /j. dA. Use...
Suppose you have a circular cross sectional wire with radius R, a resistivity of ρ, and...
Suppose you have a circular cross sectional wire with radius R,
a resistivity of ρ, and that is carrying a uniformly distributed
current of I(t) = I0 cos(ωt) (notice it changes in time).
a) Find the electric field that is generating this current using
the proper form of Ohm’s Law.
b) Find the magnetic field outside of the wire that is generated
by the current and the time changing electric field combined.
Question 2: Suppose you have a circular cross...
2. (30 points) A very long, straight, solid copper cylinder of radius R (>2R) is oriented with it...
2. (30 points) A very long, straight, solid copper cylinder of radius R (>2R) is oriented with its axis along e z-direction. The cylinder carries a current whose current density is j(r), where r is the radial distance from the cylinder axis. The current density, although symmetric about the cylinder axis, is not constant but varies with r according to 31o a) (10) Obtain an expression for the current /(in terms of Jo, r and R) flowing in a circular...
An infinitely long, straight, cylindrical wire of radius R carries a uniform current density J. Using...
An infinitely long, straight, cylindrical wire of radius R carries a uniform current density J. Using symmetry and Ampere's law, find the magnitude and direction of the magnetic field at a point inside the wire. For the purposes of this problem, use a cylindrical coordinate system with the current in the +z-direction, as shown coming out of the screen in the top illustration. The radial r-coordinate of each point is the distance to the central axis of the wire, and...
[3] A wire of radius a carries a uniform current density given by which is directed...
[3] A wire of radius a carries a uniform current density given by which is directed out of the page as shown. The wire carries a total current I. (a) Which direction does the magnetic field circulate around the wire? (circle the correct answer below). (b) Calculate the magnitude of the current density in terms of I and a (c) Showing complete details, including sketches as necessary, calculate the vector magnetic field inside the wire in terms of I, a...
Problem 5 Consider a circular wire of radius R- 2.50 mm. The wire has a current...
Problem 5 Consider a circular wire of radius R- 2.50 mm. The wire has a current density whose magnitude varies radially as J = J(r) = bra. where b = 1.34 × 1010 A-ml-4 and r (measured in meters) is the radial distance from, the central axis of the wire. Throughout the cross-section of the wire, the current-density vector is perpendicular to the cross-section (i.e, the current is along the wire) (a) Find the current through the wire (b) If...
A cylindrical conductor of a circular cross section (radius = a) carries a time-invariant current I(>0)...
A cylindrical conductor of a circular cross section (radius = a) carries a time-invariant current I(>0) directed out of the page. The line integral of the magnetic flux density vector B, along a closed circular contour C positioned inside the conductor (the contour radius r is smaller than the conductor radius a) is conductor
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor. (b) Determine the vector magnetic potential (A) both inside and outside the conductor from the relationship B V x A
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor....
b inside a current carrying wire
A steady current I flows through a wire of radius a. The current density in a wire varies with ras ) = kr2, where k is a constant and r is the distance from the axis of the wire. Find expressions for the magnitudes of the magnetic field inside and outside the wire as a function of r. (Hint: Find the current through an Ampèrian loop of radius r using thru /j. dA. Use...
Suppose you have a circular cross sectional wire with radius R,
a resistivity of ρ, and that is carrying a uniformly distributed
current of I(t) = I0 cos(ωt) (notice it changes in time).
a) Find the electric field that is generating this current using
the proper form of Ohm’s Law.
b) Find the magnetic field outside of the wire that is generated
by the current and the time changing electric field combined.
Question 2: Suppose you have a circular cross...
2. (30 points) A very long, straight, solid copper cylinder of radius R (>2R) is oriented with its axis along e z-direction. The cylinder carries a current whose current density is j(r), where r is the radial distance from the cylinder axis. The current density, although symmetric about the cylinder axis, is not constant but varies with r according to 31o a) (10) Obtain an expression for the current /(in terms of Jo, r and R) flowing in a circular...
An infinitely long, straight, cylindrical wire of radius R carries a uniform current density J. Using symmetry and Ampere's law, find the magnitude and direction of the magnetic field at a point inside the wire. For the purposes of this problem, use a cylindrical coordinate system with the current in the +z-direction, as shown coming out of the screen in the top illustration. The radial r-coordinate of each point is the distance to the central axis of the wire, and...
[3] A wire of radius a carries a uniform current density given by which is directed out of the page as shown. The wire carries a total current I. (a) Which direction does the magnetic field circulate around the wire? (circle the correct answer below). (b) Calculate the magnitude of the current density in terms of I and a (c) Showing complete details, including sketches as necessary, calculate the vector magnetic field inside the wire in terms of I, a...
Problem 5 Consider a circular wire of radius R- 2.50 mm. The wire has a current density whose magnitude varies radially as J = J(r) = bra. where b = 1.34 × 1010 A-ml-4 and r (measured in meters) is the radial distance from, the central axis of the wire. Throughout the cross-section of the wire, the current-density vector is perpendicular to the cross-section (i.e, the current is along the wire) (a) Find the current through the wire (b) If...
A cylindrical conductor of a circular cross section (radius = a) carries a time-invariant current I(>0) directed out of the page. The line integral of the magnetic flux density vector B, along a closed circular contour C positioned inside the conductor (the contour radius r is smaller than the conductor radius a) is conductor
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