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Considering Figure 4.7, suppose the area of a single loop of the pair is
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Fundamentals of Electromagnetics with Engineering Applications
- A flat, circle surface area with a radius of 4m is in the YZ-plane at x=0, Find the magnitude of the magnetic flux through this surface produced by a magnetic flux density of B=3.5ax-6.4ay+8az Tarrow_forwardA long, solid, cylindrical wire of radius A has a current density given by j = j0r/A. Determine the magnetic field, within the wire, in terms of the total current "I" flowing through the wire.arrow_forwardWhen the same current flows in the same direction in the form of two parallel straight lines separated by l, as shown in Figure 5, the twoFind the magnetic field H at the position where the distance is z0 away from the center line perpendicular to the propagation current.The thickness of the line is zero and the material of space is air.arrow_forward
- a) A circular loop of radius ? carries current ? as shown in the figure. Find the magnetic flux density ?⃗ at a point on the axis of the loop by using Biot-Savart law. Show all the details of Biot-Savart formulation b) A surface charge density exists on the hemispherical surface of the radius ? shown in the figure given as??⃗⃗ =?0????ê?A/m where ?0 is constant. i) Find the total current flowing on the surface ii) Using the solution of part (a), find the magnetic flux density ?⃗ at the origin ?.arrow_forwardTwo circular loops, L1 and L2, of radius 50 cm are carrying currents of 10 mA in thesame direction. If L1 is at z=0 and L2 at z=10 cm, find the total magnetic field due toboth loops at (0,0,50 cm). Draw neat diagrams to explain the concept.arrow_forwardSupposed that a coaxial cable consists of a solid inner conductor of radius a, surrounded by a concentric cylindrical tube of inner radius b and outer radius c as shown below. We assume that the conductors are carrying an equal current I naught that is distributed equally into the cross-section but of different directions as indicated by the directions in the image above. Calculate the magnitude of magnetic field at a distance r from the axis, where: - rc Plot the magnitude of the magnetic field with respect to the distance r from the axis.arrow_forward
- Determine the work done, in µJ, in moving a 8-nC charge from A(3, 4, 3) m to B(-3, 3, -1) m against the electric field due to an infinite sheet charge of density 6 nC/m^2 at y = -1 m.arrow_forwardConsider a point charge 3Q is located at the origin. Divergence of the electric flux density produced by the charge is ....arrow_forwardFrom two homogeneous media; Express as Νr1=2 for x<0 region and ,Nr2=72 for x>0 region is being done. Expression of magnetic field in primary medium H = 150x − 400y + 250z A/m as it is; a) Calculate the expression for the magnetic field in the second medium. b) Calculate the magnetic flux density in the primary medium. c) Calculate the magnetic flux density in the second medium.arrow_forward
- A current I0 circulates in the direction shown in the figure in a closed triangular ring with perpendicular side lengths a. If this ring is placed at a distance of 2a from a very long wire parallel to its long side and carrying a current of 2I0 as shown in the figure, what would be the net magnetic force acting on the ring?arrow_forwardConsider two coaxial solenoids with free space cores. Solenoid A is placed inside Solenoid B and solenoid B carries a current of 2I0 which creates a magnetic flux density of magnitude of B0. If the cross-sectional area, length and number of turns per length of Solenoid A are S, 4h and n respectively, calculate the mutual inductance between Solenoid A and Solenoid B.arrow_forwardAn infinitely-long, hollow, conducting cylinder carries a uniform current I that flows parallel to its axis and into the paper. Its inner radius is a and its outer radius is b. Derive expressions for the magnetic field for (a) a < r < b and (b) r > b Note: See image for the figure.arrow_forward
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