The magnitude of the magnetic field at a certain distance from a long, straight conductor is represented by B. What is the magnitude of the magnetic field at twice the distance from the conductor?
A. At twice the distance, the magnitude of the field is 4B.
B. At twice the distance, the magnitude of the field is 2B.
C. At twice the distance, the magnitude of the field is B/2.
D. At twice the distance, the magnitude of the field is B/4.
E. At twice the distance, the magnitude of the field remains equal to B.

Option C is correct.

The magnitude of the field is reduced to half at twice the distance,

Explanation:

The magnetic field produced in a long, straight conductor carrying a current I at distance r is given by

B = μ₀I/2πr

Where μ₀ is the constant permeability of free space.

If we increase the distance by twice then

B = μ₀I/2π(2r)

B = μ₀I/2πr(2)

B = B/2

Therefore, the magnitude of magnetic field is reduced by B/2 at twice the distance.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west