Magnetic Sources and Induction Homework Set Problem 1. Use the Biot-Savart law to calculate the magnetic field B at point C, the common center of semi-circular arcs AD and HJ respectively in the figure below. The two arcs, of radii R1 and R2, respectively, form part of the circuit ADJHA carrying current i. A H J D C R1 R2 i i In the figure above, use two colors to show the direction of the wire segment and the direction from the wire segment to point C. From this drawing make arguments based on the properties of the vector product about which wire segments (the two semi-circular segments and the two linear segments) which will contribute to the magnetic field.Magnetic Sources and Induction Homework Set In the space below, write the integrand that will be used. For example, if the linear segments will contribute then dl=dx. Integrate the contributions from the appropriate wire segments in the space below. Use the principle of superposition to find the total magnetic field at point C.Magnetic Sources and Induction Homework Set Problem 2. The figure shows five long parallel wires in the xy plane. Each wire carries a current i=3.0 A in the positive x direction. The separation between adjacent wires is d= 8.00 cm. In unit-vector notation, what is the magnetic force per meter exerted on each of these five wires by the other wires? • z d• d••• yddLabel the wires wire 1 through 5 from left to right. In the space below, draw the field lines from the other wires which are passing through wire 1. Be sure to use the right-hand rule Repeat these drawings for the other four wires in the space below.Magnetic Sources and Induction Homework Set For wire 1, calculate the magnitude of the magnetic emanating from the other wires in the space below. Label these as B12, B13, etc. Using the drawings of the field lines and their magnitudes, calculate the magnetic field at wire 1 from the other wires using the principle of superposition. Use the force law to calculate the force on wire 1.Magnetic Sources and Induction Homework Set For wire 2, calculate the magnitude of the magnetic emanating from the other wires in the space below. Label these as B22, B23, etc. Using the drawings of the field lines and their magnitudes, calculate the magnetic field at wire 2from the other wires using the principle of superposition. Use the force law to calculate the force on wire 2.Magnetic Sources and Induction Homework Set For wire 3, calculate the magnitude of the magnetic emanating from the other wires in the space below. Label these as B31, B32, etc. Using the drawings of the field lines and their magnitudes, calculate the magnetic field at wire 3from the other wires using the principle of superposition. Use the force law to calculate the force on wire 3.Magnetic Sources and Induction Homework Set For wire 4, use symmetry arguments to calculate the force on this wire. For wire 5, use symmetry arguments to calculate the force on this wire.Magnetic Sources and Induction Homework Set Problem 3: In the figure, the long straight wire carries a current of 30 A and the wire loop carries a current of 20 A. Calculate the resultant force acting on the loop. Assume that a=1.0 cm, b= 8.0 cm and L=30 cm. 30Aa 20A20Ab L Below, use the RH-rule and re-draw the diagram with the direction of the magnetic fields shown on each wire segment.Magnetic Sources and Induction Homework Set Below, use the RH-rule and create a free body diagram for each wire segment. Use a positive value for forces which are “up” and to the “right” on the page. Calculate the magnitude of the forces which are not eliminated by the free body diagram.Magnetic Sources and Induction Homework Set Perform algebraic notation to solve the problem.Magnetic Sources and Induction Homework Set Problem 4. The figure below shows a cross-section of a hollow cylindrical conductor of radii a and b, carrying a uniformly distributed current i. a) Show that B(r) for the range b< r <a is given by arbCalculate the cross-sectional area of the hollow cylinder. Find the current density for the hollow cylinder. (Hint: J=i/A) Calculate the cross-sectional area of hollow cylinder whose inner radius is b and whose outer radius is r. Find the current enclosed in a hollow cylinder whose inner radius is b and whose outer radius is r using its cross-sectional area and the constant current density derived above. (Hint: i=JA)Magnetic Sources and Induction Homework Set With the above current enclosed, use Ampere’s Law to calculate the magnetic field B(r). b) Show for r=a that this expression reduces to a magnetic field of a long straight wire Perform the substitution and calculate the field. Derive the magnetic field of a long straight wire with current i using Ampere’s law. Compare the above results.Magnetic Sources and Induction Homework Set c) Show for r=b that this expression give zero magnetic field. Perform the substitution and calculate the field.Magnetic Sources and Induction Homework Set Problem 5. A solenoid 1.30 meters long and 2.60 cm in diameter carries a current of 18 A. The magnetic field inside the solenoid is 23.0 mT. Find the length of the wire forming the solenoid. Convert relevant quantities to SI units. Use the expression of the magnetic field for a solenoid to calculate the total number of turns, N. Calculate the total length of wire by calculating N circumferences.Magnetic Sources and Induction Homework Set Problem 6. A long solenoid with a radius of 25 mm has 100 turns/cm. A single wire of wire of radius 5.0 cm is placed around the solenoid, the central axes of the loop and solenoid are coinciding. In 10 ms, the current in the solenoid is reduced from 1.0 A to 0.5 A at a uniform rate. What emf appears in the loop? Convert relevant quantities to SI units. Write the expression of the magnetic field of a solenoid. Calculate the rate of change in the current in A/s. With the rate of change current, calculate the rate of change of the magnetic field in the solenoid. Using the properties of solenoid calculate the area wherein there is a magnetic field.Magnetic Sources and Induction Homework Set Write an expression for the emf in terms of a constant area and a changing magnetic field. Use the quantities calculated to find the emf.Magnetic Sources and Induction Homework Set Problem 7. A square loop with 2.0 m sides is perpendicular to a uniform magnetic field with half of the area of the loop in