Mathematics
Mathematics
Problem
A square loop ABCD of side 8 cm lies flat on a horizontal table. A long straight wire passes vertically through the centre of the square carrying a current of 10 A downward (into the table). Mid-points of the four sides are labelled P (on AB), Q (on BC), R (on CD) and S (on DA). a. (a) For the given direction of current in the wire, indicate the direction of the magnetic field at each of the points P, Q, R and S. b. (b) Arrange the points P, Q, R and S in order of decreasing magnetic field strength, giving a clear justification for your order. c. (c) If the direction of current in the wire is suddenly reversed while its magnitude remains 10 A, state the changes you would observe in the directions of the magnetic fields at P, Q, R and S and explain your reasoning.Intuitive explanation
The magnetic field from a long straight current-carrying wire circles around it in concentric loops, and its strength depends only on distance from the wire. The key insight is that points equidistant from the wire (like the four midpoints P, Q, R, S) experience the same field magnitude, while the direction of the field at each point is tangent to the circle centered on the wire. By using the right-hand rule and symmetry, you can determine both the magnitude and direction of the magnetic field at any of these midpoints without calculating each one independently.
Intuitive explanation
The magnetic field from a long straight current-carrying wire circles around it in concentric loops, and its strength depends only on distance from the wire. The key insight is that points equidistant from the wire (like the four midpoints P, Q, R, S) experience the same field magnitude, while the direction of the field at each point is tangent to the circle centered on the wire. By using the right-hand rule and symmetry, you can determine both the magnitude and direction of the magnetic field at any of these midpoints without calculating each one independently.