Introduction Electromagnetic theory has two important laws relating electric cur

Question

Introduction Electromagnetic theory has two important laws relating electric currents and magnetic fields. The Biot-Savart law predicts the net field B at a chosen position P, given the spatial distribution of electric current. If a wire carrying a current I is divided into N small segments dsi, each segment makes a contribution dBi to the net field: 4 ds, The permeabilityconstant ish" 4 (dB, ds, r), the Biot-Savart law is 0 , Tm/A. In terms of the magnitudes of the three vectors (7.2) dB, If a wire is shaped symmetrically, and the point P is carefully selected, the field elements of the net field can only be calculated approximately, by explicitly summing the contributions of the N segments: (7.3) The more segments used, of course, the better the approximation, which is why integration (N oo) is preferable when it can be done. In Experiment I, you'll use Equation (7.2) to calculate the ap- proximate net field at one point inside an irregularly-shaped current loop Ampere's law also relates electric currents to magnetic fields, but much less directly (7.4) He The integral on the left is a line integral around a closed (Amperian) loop in empty space, and the current on the right side is the net current enclosed by the loop. The sign of Ia, depends on the direction of current flow and the direction of integration (clockwise or counter-clockwise), accord- ing to the usual right-hand rule.

Explanation / Answer

1. the field created by segments on the opposite sides of the pint P inside the current carrying loop is in the same direction

and the net field at point P is in the diurection of the thumb when the fingers of the right hand are culed in the direction of the current in the wire

2. a. for all the segments of same length, the segment closest to point P makes the largest contribution to the magnetic field, because magnetic field due to current follows inverse equare law, closer the point more the field

b. the fartherst segment making lest angle with the line joining the point P to the midpoint of the segment contribute least to the total magnetic field

because for low theta, sin(theta) is low and again the inverse square law means farther segmets will produce lower fields

3. magnetic field at point P = 9*10^-5 T

now, for this field radisu of loop comes out to be r

9*10^-5 = 4*pi*10^-7*5/2*r [ i = 5 A]

r = 3.49 cm

this is a reasonable approximation but, still not exact because of two reasons

the loop is not a circle

the point P is not at the center of the loop

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