Consider the following figure. (a) A conducting loop in the shape of a square of edge length -0430 m carries a current I- 11.1 A as shown in the figure above. Calculate the magnibtude and direction of the magnetic field at the centre of the square. (0) ir this conductor is reshaped to form a ciroular loop and carries the same current, what is the value of the magnetic field at the centre Step 1 As shown in the drawing below, the magnetic field is directed into the page from the clockwise current. If we consider the sides of the square to be sections of four wires of infinite length, we expect the magnetic field at the centre of the square to be less than four times the strength of the field at a point /2 away from a wire of infinite length with current I. Using the Biot-Savart law, we can find the fleld from a current in a wire of infinite lenngth, and this tells us that where a is the distance from the wire to the point where the field is measured, Forming the wire into a circle would not change the magnetic field in the centre by a large amount since the average distance from the centre to the wire is not much different for the circle than for that of the souare. Step 2 Each side of the square is a section of a thin, straight conductor, so we will use the solution derived from the Biot-Savart law to calculate the magnetic fleld at the centre of the square. We will also use this result from the Biot-Savart law to derive the equation for the magnetic field at the centre of a circular loop of circumference carrying current 1. (a) We use the equation derived from the Biot-Savart law for the fleld created by a thin straight wire. Each side contributes a field pointing away (into the page) at the centre, so together they produce the following magnetic field, where a is the distance to the wire from the centre of the square, and is a constant, the permeability of free space. The result for the four wires is given by the following. - (an- an(-) (se x 10-7T m/AX *( Ox m) Taking the centre of the square to be the origin of the y plane, and taking the positive z axis to be pointing perpendicularty out of the page toward us, we have i-( OVax 10-5T - -(O