A conducting w ire carrying a steady current I is shaped as shown in thefigure below. All connected straight segments meet at right angles. Whatis the magnetic moment of the current loop?I abbaˆiˆjˆk(a)Iab (ˆj + ˆk)(b)Iab (ˆj − ˆk)(c)√2Iab (ˆj + ˆk)(d)Iab (ˆk − ˆj)11
Question
A conducting w ire carrying a steady current I is shaped as shown in thefigure below. All connected straight segments meet at right angles. Whatis the magnetic moment of the current loop?I abbaˆiˆjˆk(a)Iab (ˆj + ˆk)(b)Iab (ˆj − ˆk)(c)√2Iab (ˆj + ˆk)(d)Iab (ˆk − ˆj)11
Solution
The magnetic moment (μ) of a current loop is given by the product of the current (I) and the area (A) of the loop. The direction of μ is perpendicular to the area of the loop, following the right-hand rule (thumb in the direction of the current, fingers curl in the direction of μ).
The area of the loop in the figure is ab, and the current is I. The direction of the magnetic moment is along the negative y-axis (ˆj) and the positive z-axis (ˆk), because the current is flowing in the clockwise direction when viewed from the positive z-axis.
Therefore, the magnetic moment of the current loop is Iab (ˆj + ˆk), which corresponds to option (a).
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