Final answer:
The magnetic field at the center of a coil made from a wire is minimum when the coil is circular. For a long straight wire, the strength of the magnetic field is a function of current and distance, whereas for a coil, the Biot-Savart Law is used to calculate the magnetic field at the center.
Step-by-step explanation:
The magnetic field at the center of a coil formed from a wire of length l will be minimum when the coil is in the shape of a circle. This is because the circular shape ensures that the magnetic field lines are symmetrical and uniformly distributed. According to the Biot-Savart Law, the magnetic field (B) at the center of a circular loop carrying current I is given by μ0I/2R, where μ0 is the permeability of free space and R is the radius of the loop. The right-hand rule also helps us determine the direction of the magnetic field: if the thumb of our right hand points along the direction of the current, the fingers will curl in the direction of the magnetic field created by the current-carrying wire.
For a long straight wire, the magnetic field strength is proportional to the current (I) and inversely proportional to the distance (r) from the wire, as described by the equation B = μ0I/(2πr). In cases such as a finite length of wire or a cylindrical wire with varying current density (J = cr), the magnetic field can be calculated using variations of the Biot-Savart Law or by employing Ampère's Law. For the straight wire, the magnetic field lines form concentric circles around the wire, decreasing in strength with increasing distance from the wire.