You are standing 20 cm directly away from from the mid-point of a long, straight current carrying wire that runs east/west and are experiencing a magnetic field B1 due to the wire. If you were to move a new location that is 7 cm to the east of your initial location and 5 cm closer to the wire, you would experience a magnetic field of:

B1, 0.588 B1, (1/9)B1, 3.27 B1, 6.1 B1, 1.33 B1, (1/6) B1, 1.54 B1

To determine the magnetic field at the new location, we can apply the Biot-Savart law, which relates the magnetic field produced by a current-carrying wire at a point in space.

The Biot-Savart law states that the magnetic field (dB) produced by a short section of a current-carrying wire is proportional to the product of current (I), the length of the wire element (ds), and a vector pointing from the element to the point of interest (r). Mathematically, it can be written as:

dB = (μ₀/4π) * (I * ds) * (sinθ / r²)

where μ₀ is the permeability of free space, θ is the angle between the wire element and the vector r, and r² is the square of the distance between the wire element and the point of interest.

In our case, we are given that the wire is carrying a current and we need to compare the magnetic field at two different points. Let's calculate the magnetic field at the initial location (20 cm away from the wire's midpoint) and the new location (7 cm east and 5 cm closer to the wire).

1. Initial location:
At the initial location, we are 20 cm away from the wire's midpoint. Since the wire is straight, the magnetic field will be perpendicular to the line connecting the point of interest and the wire's midpoint. Therefore, the angle θ = 90° (or π/2 radians).
The equation for the magnetic field at the initial location can be simplified to:

dB₁ = (μ₀/4π) * (I * ds) / r₁²

Here, r₁ represents the distance between the wire element and the initial location. Since the equation is proportional to 1/r₁², we only need to consider the relative distance between the two locations.

2. New location:
At the new location, we are 7 cm east of the initial location and 5 cm closer to the wire. The total distance from the wire's midpoint to the new location is 15 cm (20 cm - 5 cm).
Again, the wire is straight, so the magnetic field will be perpendicular to the line connecting the point of interest and the wire's midpoint. The angle θ = 90° (or π/2 radians) as well.
The equation for the magnetic field at the new location can be simplified to:

dB₂ = (μ₀/4π) * (I * ds) / r₂²

Here, r₂ represents the distance between the wire element and the new location. Since the equation is proportional to 1/r₂², we only need to consider the relative distance between the two locations.

Finally, to compare the magnetic fields at the two locations, we need to calculate the ratio of dB₂ to dB₁:

dB₂ / dB₁ = (r₁/r₂)²

Substituting the relative distances:

dB₂ / dB₁ = (20 cm / 15 cm)²

Now, we can calculate the value of (20 cm / 15 cm)²:

(20 / 15)² = 1.7778

Therefore, the magnetic field at the new location is approximately 1.778 times the magnetic field at the initial location.

In terms of the given options, the magnetic field at the new location is closest to 1.778 B₁.