Chapter 8.1, Problem 8.1P

9.3. A system of two conductors has a cross section given by the intersection of two circles of radius b with centers separated by 2a as shown in figure below. The conducting portion is shown hatched, the non-hatched lens-shaped region being a vacuum. The conductor on the left carries a uniform current density, J1, coming out of the page, and the conductor on the right carries a uniform current density, −J 12, going into the page. Assume that the magnetic permeability of the conductor is the same as that of the vacuum. Find the magnetic field at all points in the vacuum enclosed between the two conductors. 2a

You want make the largest possible B field at some location (some point in space) by running acurrent through a piece of copper wire of length L that you already have, with a battery of voltage Vthat you also already have. What is the best possible shape and size for the wire to take on? Whatis the largest B (an equation) based on V, L, resistivity of copper (ρ), and any other parameters -geometric or otherwise - that can be created?

Ps Two Conductancas G ard 62 haring valnes of b0o and Joo yn S respectiny , are connactid in pavallil. The Combination is then Gonmeetid in parallal with 800 resistor. Calculate the s a) Eguiralant re wistanca ofthe parallal Circnit. [Ans: 363. 6352 b) Curant in each branch if Gq Carries 2mA. Ans: SA 4.16 m power diss ipatid in coah draned. [Anso 6.6mw,lomw13-8mm d) Voltage across each omponant-LAnse 3.33. e) Total power dissipatol-(Ans: 30.5 mn). Pt A 6v battey, delivers loMA to thvee vesistors in faralkel , R, 21kr, R2=2k2,R3=Rx. Caleulatas a) Curront in Rx sthat is Ix. [Anss I mÁ) b) Power dissipatid. by Rx and Ry-{Anss 6mw, 36 mm. C) Resistance vatio Rx/R--(Anst 615). d) Cuvrent vatio Ji/Ix- [Anss 6/4]-

Find the magnetic vector potential of a finite segment of straight wire, carrying current a current I.

A long straight co-axial cable with three coaxial conductors of negligible resistance lies along the z-axis. The radii of the conductors are as shown in Fig. 3 (b). The inner conductor and outer conductor each carry currents I/2 [A] in -2 direction. The intermediate conductor carries current I [A] in 2 direction. Assuming the current distribution is uniform in each conductor, find the H as a function of distance from the center, r of the following regions: i. 0 C, bi Fig. 3 (b)

Example 7.10. A short solenoid (length / and radius a, with n₁ turns per unit length) lies on the axis of a very long solenoid (radius b, n₂ turns per unit length) as shown in Fig. 7.32. Current I flows in the short solenoid. What is the flux through the long solenoid? a ಮು FIGURE 7.32

Consider an infinitely long hollow cylindrical wire, of inner radius R1 and outer radius R2, and carrying a uniform current density amounting to a total current I. Use Ampère's law to determine the B-field in every point at a distance r from the wire's central axis, both within the wire as outside of it.

Two straight, parallel, superconducting wires 7.06 mm apart carry equal currents of 12958 A in opposite direction. Calculate the force experienced in a 0.5m length. Final answer should be in two (2) decimal places. Express your answer in exponential form. For Example: - 1.13 x 10-4 should be answerd as 1.13e-4. 5.00 x 10³ should be expressed as 5.00e+3. O