Question

How does the magnitude of magnetic field around a long Straight current carrying wire of radive B depend on radial distan RAR from the lang gxis of wire ? Assuming that the cpirent is steady and uniformly distribe within N the wire, How does the field magnitude che on the radial distance rak from the wire axis-

Answer 1

e lo current through the cylinder in the form of circular magnetic lines of force, with their centres lying on the axis of cylinder. These lines of force are perpendicular to the length of cylinder Case I. Point P is lying outside the cylinder. Letr be the perpendicular distance of point P from the axis of cylinder, where > R Let B be the magnetic field induction at P. It is acting tangential to the magnetic line of force at P directed into the paper. Here Band dl are acting in the same direction 000000 W4. FIGURE 3(a).23 W Applying Ampere circuital law we have or O B dl cos 0º = Mol or O B dl = 4,1 or B 2 r = Mol Ho! B = 211 เ.. Ba 1/1 Case II. Point P is lying inside cylinder. Here <R We may have two possibilities. (i) If the current is only along the surface of cylinder which is so if the conductor is a cylindrical sheet of metal, then current through the closed path L is zero. Using, Ampere circutal law, we have B = 0 (ii) If the current is uniformly distributed throughout the cross-section of the conductor, Then the current through closed path L is given by = X = I - ? R² NR²

3/16 Appiving Ampere's circuital law, we have or 20TB = Mou, I' = - Mol, IP R? . HOU, IT B =- 2a Rē ie, Bar If we plot a graph between magnetic field induction B and distance from the axis of cylinder for a current flowing through a solid cylinder, we get a curve of the type as shown in Fig. 3(a).24. BE----- Bar Bag FIGURE 3(a):24 Here we note that the magnetic field induction is maximum for a point on the surface of solid cylinder carrying current and is zero for u point on the axis of cylinder.