Physics · Moving Charges And Magnetism · NEET
No, it goes down. When you make more turns from a fixed wire, each turn becomes smaller. If total length is L, one turn has radius r and area proportional to r squared. With N turns, each turn uses length L/N, so its radius is r/N and its area is (r/N) squared, which is A/N squared. Then m = N times I times A/N squared = IA/N. So m falls as 1/N. More turns from the same wire always means a smaller moment.
N is total wire length divided by one loop's perimeter. A square of side a has perimeter 4a. So N = 12a / 4a = 3 turns. For a triangle of side a, perimeter is 3a, so N = 12a / 3a = 4 turns. Always divide total length by the shape's perimeter to get how many complete loops you can wind.
The circle. For a fixed length of wire (fixed perimeter), a circle encloses the most area, then a square, then an equilateral triangle. Since m = NIA and the circle packs the largest area into one turn, it gives the largest moment. This is the isoperimetric idea: more sides (up to a circle) enclose more area for the same perimeter.
Both, but for different jobs. Use the perimeter to find N (turns = total length / perimeter). Use the area of one single turn in m = NIA. Students often mix these up. The perimeter never enters the moment directly; it only tells you how many turns you can make.
A uniform conducting wire of length 12a and resistance R is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side a, (ii) a square of side a. The magnetic dipole moments of the coil in each case respectively are:
A 2 A current is flowing through two different small circular copper coils having radii ratio 1 : 2. The ratio of their respective magnetic moments will be:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
m = NIA, where N is the number of turns, I is the current in amperes, and A is the area of one turn in square metres. The unit of m is ampere metre squared (A m²) and its direction is given by the right-hand rule, along the axis of the coil.
Because both N and A change. A fixed wire length can be wound into more turns of a smaller shape (raising N but cutting A), or fewer turns of a larger shape. Since m = NIA depends on the actual area enclosed, the shape that encloses the most area per unit perimeter (the circle) gives the highest moment.
No, resistance is not in the formula m = NIA. Resistance only matters if the question asks for the current through a given voltage. Once the current I is fixed, the moment depends only on N and A.
Curl the fingers of your right hand along the direction of current flow in the loop; your thumb points along the magnetic moment vector, perpendicular to the plane of the loop. This is the same as the direction of the magnetic field on the loop's axis.
