In Fig. 29-4, a wire forms a semicircle of radius and two (radial) straight segments each of length . The wire carries current . What are the(a) magnitude and(b) direction (into or out of the page) of the net magnetic field at the semicircle’s center of curvature C?
The magnitude of the magnetic field B at centre of circular arc, of radius R, and central angle , carrying a current I is given as follows:
For a straight conductor consider the formulas:
Here, is the magnetic field through the current carrying conductor, length of the element and is unit vector that is a point from the element to the given point.
To calculate the magnetic field due to current for left straight segment as follows:
Calculate the magnetic field due to current for a right straight segment as follows:
Calculate the magnetic field due to current from circular section as follows
So, the total magnetic field at the center of semicircle arc is
Hence the magnetic field is, .
Using the right hand rule, direction of magnetic field is into the page
Figure 29-25 represents a snapshot of the velocity vectors of four electrons near a wire carrying current i. The four velocities have the same magnitude; velocity is directed into the page. Electrons 1 and 2 are at the same distance from the wire, as are electrons 3 and 4. Rank the electrons according to the magnitudes of the magnetic forces on them due to current i, greatest first.
The current density inside a long, solid, cylindrical wire of radius a= 3.1mm is in the direction of the central axis, and its magnitude varies linearly with radial distance r from the axis according to where . (a) Find the magnitude of the magnetic field at role="math" localid="1663132348934" , (b) Find the magnitude of the magnetic field , and(c) Find the magnitude of the magnetic field .
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