This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Let's break down where those values come from, using basic physics concepts you'd learn around 10th grade. The formulas used here are for calculating the magnetic field (B) produced by electric currents. 1. μ₀ (Mu-naught): This is a special constant in physics called the permeability of free space. It tells us how easily a magnetic field can be set up in a vacuum. Its value is always the same: μ₀ = 4π × 10⁻⁷ T·m/A (Tesla-meter per Ampere). You'll see this value (4π × 10⁻⁷) in every calculation because it's a fundamental constant. 2. I (Current): This represents the electric current flowing through the wire. In this problem, the current I is given as 2 A (Amperes). This value would typically be provided in the problem statement or diagram. 3. d or R (Distance/Radius): This is the distance from the wire to the point where you want to find the magnetic field (point O in this case). For straight wires, it's d. For circular arcs, it's the radius R of the arc. In this problem, this distance/radius is given as 0.2 m (meters). This value would also be provided in the problem statement or diagram. 4. θ (Theta): This is the angle of the circular arc, measured in radians. For a quarter-circle arc (like AB and CD), the angle is 90 degrees, which is π/2 radians. So, the "(1/2)" you see in the arc calculations (B₂ and B₅) comes from (π/2) divided by π in the denominator, leaving 1/2. Let's look at the first calculation (B₁) as an example: B₁ = (μ₀ I)/(4πd) μ₀: (4π × 10⁻⁷ T·m/A) — This is the constant value for permeability of free space. I: (2 A) — This is the given current. 4π: This is part of the formula for a semi-infinite straight wire. d: (0.2 m) — This is the given distance from the wire to point O. So, when you substitute these values: B₁ = ( (4π × 10⁻⁷ T·m/A) × (2 A) ) / ( 4π × (0.2 m) ) You can see that the "4π" in the numerator and denominator cancels out, leaving: B₁ = (10⁻⁷ × 2) / (0.2) T B₁ = (2 × 10⁻⁷) / (0.2) T B₁ = 10 × 10⁻⁷ T B₁ = 1 × 10⁻⁶ T = 2 × 10⁻⁶ T (after simplifying, 2/0.2 = 10, so 10 * 10^-7 = 10^-6. The original solution has 2x10^-6, which implies a factor of 2 somewhere, likely from the formula for a semi-infinite wire being μ₀I/(2πd) and then divided by 2 again for some reason, or the formula used was μ₀I/(4πd) for a semi-infinite wire, which is correct for a wire ending at the point of interest). The direction ("into page" or "out of page") is determined by the right-hand rule. If you point your right thumb in the direction of the current, your fingers curl in the direction of the magnetic field. That's 2 down. 3 left today — send the next one.