Magnetic Field Around a Wire?

📌 CONCEPT: The magnetic field around a current-carrying wire is a result of the interaction between the moving charges and the magnetic field, as per the Biot-Savart Law.

📐 RULE / FORMULA: According to the Biot-Savart Law, the magnetic field (B) at a point due to a current-carrying wire is given by B = μ0 × I / 2πr, where μ0 is the magnetic constant, I is the current, and r is the distance from the wire.

💡 WORKED EXAMPLE: Consider a wire carrying a current of 2 A, bent into a circular shape with a radius of 0.2 m. If the magnetic field at the centre of the circle is 4 × 10^-7 T, we can use the formula to find the magnetic field at a point on the circumference, 0.1 m away from the centre. First, we rearrange the formula to solve for the magnetic field: B = μ0 × I / 2πr. Substituting the values, we get B = (4π × 10^-7) × 2 / (2π × 0.1).

⚠️ COMMON MISTAKE: Students often forget to consider the direction of the magnetic field, which is tangential to the circle and in the direction of the thumb of the right-hand rule, where the thumb points along the current direction and the fingers indicate the magnetic field direction.