G semi-infinite wire segment that lies along the negative y axis and carries current of 548 Amperes in the positive y direction. Using the Biot-Savart law and showing your logic, determine just the DIRECTION of the magnetic field produced at point P located at (4.5 cm, 0, 0)

The magnetic field at a point (4.5, 0, 0) from the wire lying in the negative y-axis, with current flowing in the positive y-direction is directed in the positive z-direction.

Explanation:

The Biot Savart Law explains that the magnetic field experienced as a result of a wire of a particular length at a point r, from the wire is given as

dB = (μ₀/4π) ∫ (ds × ř)/r²

where ds = direction vector for the flow of current

ř = unit vector in the direction of the point where the magnetic field is required.

r = magnitude of the direction vector from the wire, to the point where the magnetic field is required.

Basically, the magnetic field is an integral sum of the vector product of ds and the unit vector in the direction of the point r where the magnetic field is required at that point all multiplied with (μ₀/4πr²)

This question requires only the direction of this magnetic field. This would be obtained from just the vector product of ds and ř.

ds = positive y-direction = (0, ds, 0)

wire segment that lies along the negative y axis and point P is located at (4.5 cm, 0, 0)

r = (4.5, 0, 0) - (0, -y, 0) = (4.5, y, 0)

Since we're not concerned about the magnitude, we can write the unit vector as

ř = (x, y, 0)

Direction of B is obtained from

(0î + dsj + 0k) × (xî + yj + 0k)

=

| î j k |

|0 ds 0|

|x y 0|

= î(0 - 0) - j(0 - 0) + k(xds- 0)

= 0î + 0j + xdsk

This means that the magnetic field at a point (4.5, 0, 0) from the wire lying in the negative y-axis, with current flowing in the positive y-direction is directed in the positive z-direction.

Hope this Helps!!!