To calculate the current density in the wire, you need to determine the cross-sectional area of the wire and divide the current by that area. Here's how you can do it:
Calculate the radius of the wire: The diameter is given as 1.02 mm, so the radius (r) can be found by dividing the diameter by 2: r = 1.02 mm / 2 = 0.51 mm = 0.51 × 10^-3 m
Calculate the cross-sectional area (A) of the wire: The formula for the area of a circle is A = πr^2, where π is approximately 3.14159. A = 3.14159 × (0.51 × 10^-3 m)^2 = 8.192 × 10^-7 m^2
Calculate the current density (J): The current density (J) is given by the formula J = I / A, where I is the current. J = 250 A / 8.192 × 10^-7 m^2 ≈ 3.05 × 10^8 A/m^2
Therefore, the current density in the wire is approximately 3.05 × 10^8 A/m^2.