Question

Vladimirkezerashvili, Ph.D. Student's name ase show all your work. Answers without adequate work will receive no credits Carry out all the units throughout the lations. Show the numeric answers with the appropriate number of significant figures and units. Box the final answers. 15 points). A wire, in a plane, has the shape shown in figure. The radii of the semicircular segments are 20.0 cm and 30.0 cm. Current I 60.0 A. Find (a) (10 points) magnitude and (a) (5 points) direction of the magnetic field at the semicircles center A (15 points) A coaxial cable consists of a solid inner conductor of radius R, surrounded by a concentric cylindrical tube of inner radius R, and outer radius R, (see the figure). The conductors carry equal and opposite currents lo distributed uniformly across their cross sections. Let I, 3.00 A. R, 0.60 mm, R 4.00 mm, and R, 4.80 mm. Find B for (a) (10 points) r 2.00 mm: (b) (5 points) r= 5.00 mm 3. (15 points) A 400 turn solenoid 5.0 cm long, has a circular cross section of 0.75 cm. A 20 turn coil is wound tightly around the center of the solenoid. If the current in the solenoid is changing accoeding to I 6.0(1 +e) A, what will be induced current in the short coil at t 0.50s if the resistance of the short coil is 0.0015 27 4. (15 points) A 20 m long wire stretches along z axes and carries 10 A current down (-z). The wire passes through uniform magnetic fieldB-(.10i-40j+20k) T. Determine the components of the force on the wire. 5 (15 points) a) (10 points) Determine the equivalent resistance of the "ladder" of equal 30 2 resistors shown in figure, in other words, what resistance would an A-MW ohmmeter read if connected between points A and B? b) (5 points) What is the power dissipated in the upper resistors on the left (the one connected to point A) if a 41 V battery is connected between points A and B? R R BR R B-W (10 points) If the resistance of the resistor in figure is slowly decreased, a) (5 points) what is the direction of the field induced, and b) (5 points) what is the direction of the current induced in the small circular loop inside the larger loop? 6. 7. (15 points). A rectangular loop of wire is placed next to a straight wire at the distance d6.0 cm as shown in figure (a20.Ocm, b 10.0cm) There is a current of 10 A in both wires. Determine a) (10 points) the magnitude and a) (5 points) direction of the net force on the loop

Answer 1

1a] Net magnetic field at center = (u0 I /4a - u0 I/b) where a and b are the radii of semicircular segments

= pi*10^-7*60/0.20 - pi*10^-7*60/0.30

= 3.14*10^-5 T

b] direction will be determined by the direction of magnetic field of smaller semicircle

= into the page

2a) magnetic field B = u0i_enclosed/2pir

= 2e-7*3/2e-3 = 0.0003 T

b) again magnetic field B = u0i_enclosed/2pir

= 2e-7*(3 -3)/2e-3

= 0 T