The integral in this question must be approximated using a numerical method, suc

Question

The integral in this question must be approximated using a numerical method, such as Simpson's rule.

By the Biot-Savart law, the component along a unit vector

The integral in this question must be approximated using a numerical method, such as Simpson's rule. By the Biot-Savart law, the component along a unit vector e of the magnetic field BCxo, yo, zo) of a current-carrying wire given by a curve C, is X e BOxo, yo, zo) e dr where I is the current (I is positive if the current is in the orientation of C) R C (xo, yo, zo) R IRl. and Ao is a constant. If x, y, and z are in meters, the current is 10 amperes, and Ho 4T x 10 then the z-component of the magnetic field at (0,0, in the case that the current loop is the 3-leaf rose in the x, y plane r cos 30, 0 S 6 S T, in micro-Teslas, is (A) -0.421652 (B) 0.588452 (C) 0.727333 (D) -0.879622 (E) -0.868012 (F) -0.688375 (G) -0.574072 (H) -0.782921

Explanation / Answer

In this special case the symmetry is such that the current elements around the circumference add directly at the centre. The line integral of length is just the circumference of the circle.

Biot–Savart law : a statement in electromagnetism: the magnetic intensity at any point due to a steady current in an infinitely long straight wire is directly proportional to the current and inversely proportional to the distance from point to wire .

B) -0.588452

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