A hollow cylindrical pipe of outer radius R and inner radius a carries a uniform current densityJ. Using Ampere's Law, derive an expression for the magnetic field at a point inside the conducting material at a distance r (where a
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![A hollow cylindrical pipe of outer radius R and inner radius a carries a uniform
current density J. Using Ampere's Law, derive an expression for the magnetic field
at a point inside the conducting material at a distance r (where a<r<R) from the
centre of the pipe.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed4162e7-c43a-41f9-89d0-c16de8b74d1d%2F28428f0f-86bf-4683-b06e-0e27df6f0a3e%2F133rqjc_processed.png&w=3840&q=75)
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- Problem 7: A square loop of side length a =3.6 cm is placed a distance b = 0.65 cm from a long wire carrying a current that varies with time at a constant rate, i.e. I(t) = Qt, a where Q = 3.4 A/s is a constant. Part (a) Find an expression for the magnetic field due to the wire as a function of timet at a distance r from the wire, in terms of a, b, Q, t, r, and fundamental constants. Expression : B(t) = Select from the variables below to write your expression. Note that all variables may not be required. B, y, Ho, T, 0, d, g, h, j, m, n, P, Q, r, t Part (b) What is the magnitude of the flux through the loop? Select the correct expression. SchematicChoice : HoQat In 27 HoQa In HOQat 1 1 In (b+a)2 h2 HoQa In 1 1 HoQat HOQat In In 6+ a Ф— (b+ a)² (b+a)2 12 2т h2 Part (c) If the loop has a resistance of 3.5 Q, how much induced current flows in the loop? Numeric : A numeric value is expected and not an expression. I = Part (d) In what direction does this current flow? MultipleChoice : 1)…Figure (a) shows an element of length ds = 1.26 um in a very long straight wire carrying current. The current in that element sets up a differential magnetic field aB at points in the surrounding space. Figure (b) gives the magnitude dB of the field for points 3.6 cm from the element, as a function of angle between the wire and a straight line to the point. The vertical scale is set by dB = 60.0 pT. What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance 3.6 cm from the wire? Number i Units dB (pT) dB₂ 0 μT (a) π/2 9 (rad) (b) Wire 2Anil
- Consider two thin wires of length w with a uniform current I as shown in figure below. Determine the magnetic flux density B(F) at the point P(w,w,0). Show the direction of the magnetic flux density at the given point. W I Z W P(w,w,0) yExtremely large magnetic fields can be produced using a procedure called flux compression. A metallic cylinder tube of radius R is placed coaxially in a long solenoid of slightly larger radius. The space between the solenoid and the tube is filled with a highly explosive material. When the explosive is detonated, it causes the tube to implode into a cylinder of radius r < R. If the implosion happens too quickly, the current induced in the tube maintains an almost constant magnetic flux within it. If the initial magnetic field on the solenoid is 2.50 T and R/r = 12.0, what is the maximum value that the magnetic field can reach? (Answer in T and up to the units house)A conducting cylinder has radius ?a and volume current density J1=κr in the direction of the axis of the cylinder where κ is known. It is coaxial with a conducting cylindrical shell which has inner radius b and outer radius c. Suppose we have already determined that the magnetic field outside both cylinders is zero. If the outer cylinder has a current density of J2=αr, find α. Find the magnetic field in each possible region B(r<a) = B(a<r<b) = B(b<r<c) =
- A toroid has a major radius R and a minor radius r and is tightly wound with N turns of wire on a hollow cardboard torus. Figure shows half of this toroid, allowing us to see its cross section. If R >> r, the magnetic field in the region enclosed by the wire is essentially the same as the magnetic field of a solenoid that has been bent into a large circle of radius R. Modeling the field as the uniform field of a long solenoid, show that the inductance of such a toroid is approximatelyAn infinite length line carries current I in the +az direction on the z-axis, and this is surrounded by an infinite length cylindrical shell (centered about the z-axis) of radius a carrying the return current I in the -az direction as a surface current. Find expressions for the magnetic field intensity everywhere. If the current is 1.0 A and the radius a is 2.0 cm, plot the magnitude of H versus radial distance from the z-axis from 0.1 cm to 4 cm.