Magnetic Field of a Current Carrying Loop?

📌 CONCEPT: The magnetic field at the centre of a circular loop carrying current is zero due to the equal and opposite magnetic fields generated by the inner and outer loops of the coil.

📐 RULE / FORMULA: According to Ampere's law, the magnetic field at the centre of a circular loop is given by B = (μ0  I)/(2r), where μ0 is the magnetic constant, I is the current, and r is the radius of the loop.

💡 WORKED EXAMPLE: To find the magnetic field at the centre of a circular loop carrying a current of 2A (loop 1) and 4A (loop 2) in opposite directions, we can first calculate the magnetic field due to each loop using the formula B = (μ0  I)/(2r). Since the loops are coaxial and currents are in opposite directions, the total magnetic field at the centre of the loop will be zero.

⚠️ COMMON MISTAKE: Students often forget to consider the direction of the magnetic fields generated by the loops and the relative strengths of the currents, which can lead to incorrect calculations of the total magnetic field.