G You are near a long straight current-carrying wire, and you measure the magnetic field due to the current in the wire at a location a distance d from the wire. If you move to a point 2d away from the wire and measure the magnetic field due to the current in the long straight wire, how will the magnitude compare to the field d away from the wire

B_2 / B_1 = 0.5 , Half of magnetic field at distance d.

Explanation:

Given:

- A current carrying conductor produces a magnetic field = B_1  @ r = d

- A current carrying conductor produces a magnetic field = B_2  @ r = 2*d

Find:

Compare the the magnetic Field at two points r = d and r = 2*d:

Solution:

- The magnetic Field of long current carrying wires are expressed as follows:

                                      B = u_o*I / 2*pi*r

Where,

B = Magnetic Field

I = The current in the conductor

r = The radial distance from the center of the wire.

u_o = Permittivity of free space (constant)

- Now compute B_1 and B_2:

                                    B_1 =   B = u_o*I / 2*pi*d

                                    B_2 =   B = u_o*I / 4*pi*d

- Take a ratio of B_2 to B_1:

                                    B_2 / B_1 = (u_o*I / 4pi*d) * ( 2*pi*d/u_o*I)

                                    B_2 / B_1 = 0.5

- Hence, the magnetic field at distance 2d is half of the magnetic field at distance d.

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