In this example we will use B = mu_0 I/2 pi r to calculate the distance from a w

Question

In this example we will use B = mu_0 I/2 pi r to calculate the distance from a wire that is associated with a particular magnetic field. Specifically, a long, straight wire carries a current of 100 A. At what distance from the wire is the magnitude of the magnetic field from the current equal to the magnitude of earth's magnetic field, which is about 5.0 Times 10^-5 T? We need to find the distance r at which the magnitude of the field B_wire from the current in the wire equals the magnitude of the field B_earth from the earth. Setting B_wire = B_earth, we find that B_earth = p_0 I/2 pi r We solve this equation for the distance, r, from the wire: r = mu_0 I/2 pi B_earth = (4 pi Times 10^-r T m/A)(100 A)/2 pi (5.0 Times 10^-6 T) = 0.40 m The magnetic field of the wire at a distance of half a meter is comparable in magnitude to the earth's field At what distance from a wire carrying a current of 30 A would the wire create a magnetic field with the same magnitude as the earth's? Express your answer to two significant figure and include appropriate units.

Explanation / Answer

USing , B = (u0 I ) / (2 pi R)

5 x 10^-5 = (4pi x 10^-7 x 30 ) / (2pi R)

R = 0.12 m

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