A 2.0-m-long wire carries a current of 8.2 A and is immersed within a uniform ma

Question

A 2.0-m-long wire carries a current of 8.2 A and is immersed within a uniform magnetic field B? .

When this wire lies along the +x axis, a magnetic force ???=(?2.5 ???) ?? acts on the wire, and when it

lies on the +y axis, the force is ???= ( 2.5 i^- 5.0 k^ ) N. Find all components (x,y,z) of B?

Explanation / Answer

Force on a current carrying wire places in a uniform magnetic field is given by F=IL X B-----------------------equation 1 here I=8.2A and L=2m ==> IL= 16.4A-m Let us consider B= ai+bj+ck First case: When current wire placed along X-axis ------------------------------------------------------------------- IL=16.4i B= ai+bj+ck F= 2.5j substitute these values in equation 1 F=IL X B 2.5j=16.4i X(ai+bj+ck) we know thhat i X i=0, i X j=k and i X k=-j 2.5j=b*16.4k-c*16.4j =====> b should be zero to satisfy this equation and c=-2.5/16.4=-0.1524 second case: When current wire placed along Y-axis ---------------------------------------------------------------------------- IL=16.4j B= ai+bj+ck F= -2.5i-5.0k substitute these values in equation 1 F=IL X B -2.5i-5.0k=16.4j X(ai+bj+ck) we know thhat j X j=0, j X i=-k and j X k=i -2.5i-5.0k= c*16.4i-a*16.4k after comparing similar terms we get c= -0.1524 a=5/16.4=0.3048 B=0.3048i-0.1524k

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