198 Sources of the Magnetic FieldP30.30(a)See Figure (a) to the right.(b)At a point on the zaxis, the contribution from each wire hasmagnitude BIaz=+µπ0222and is perpendicular to the linefrom this point to the wire as shown in Figure (b). Combiningfields, the vertical components cancel while the horizontalcomponents add, yieldingBIIzIzy=+FHGIKJ=++FHGIKJ=+22000θsinejThe condition for a maximum is:dBdzIz zIy=−+++=02020af, or 00I−+=Thus, along the zaxis, the field is a maximum at da=.(Currents are into the paper)Figure (a)Figure (b)FIG. P30.30Section 30.4The Magnetic Field of a SolenoidP30.31BNI=0Aso IBn==××⋅=−−047100 100400101 00031 8...T m4 TmAmA*P30.32Let the axis of the solenoid lie along the y–axis from y=0 to y=A. We will determine the field atya=. This point will be inside the solenoid if 0<<aAand outside if a<0 or a>A. We think ofsolenoid as formed of rings, each of thickness dy. Now Iis the symbol for the current in each turn ofwire and the number of turns per length is NAFHGIKJ. So the number of turns in the ring is
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