12:59 PM 0-110 points 19.P023 An eight turn coll encloses an elliptical area hav

Question

12:59 PM 0-110 points 19.P023 An eight turn coll encloses an elliptical area having a major axis of 40.0 cm and a minor axis of 30.0 cm (Fig. P19.23). The col lies in the plane of the page and has a 5.95 A current flowing clockwise around it. If the coll is in a uniform magnetic feld of 2.09 x 104 T, directed toward the left of the page, what is the magnitude of the torque on the coll? (Hint: The area of an ellipse is A - ?ab, where a and b are, respectively, the semimajor and semiminor axes of the ellipse.) N-m Figure P19.23 10. 19.P.026 A copper wire is 10.00 m long and has a cross-sectional area of 1.00 x 104 m2. This wire forms a one turn loop in the shape of square and is then connected to a battery that applies a potential difference of 0.300 V. If the loop is placed in a uniform magnetic field of magnitude 0.300 T, what is the maximum torque that can act on it? The resistivity of copper is 1.7 x 108 2-m. N-m

Explanation / Answer

The magnetic moment of the loop is given by:

M = AI n

A = pi ab (area of the loop)

I = current

n = number of turns

M = 3.141592 x 0.40 x 0.30 x 5.95 x 8

= 17.944 Am2

Given external magnetic field B = 2.09 x 10-4 T

Hence, magnitude of torque = M x B = MBsin(90) (as B and M are perpendicular)

Torque = 17.944 x 2.09 x 10-4 = 3.75 x 10-3 Nm

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