Magnetic field of a linear conductor

[gsan]

Anyone can tell me why there is a -ve for the z= -r cot theta for the picture shown below? thanks!

 

[Defennder]

Because z is negative with respect to the horizontal line passing through the linear conductor which I take to be z=0.

 

[astrokreng]

The negative sign in the expression -r cot theta indicates the direction of the magnetic field produced by a linear conductor. The z-axis is typically defined as the direction perpendicular to the plane of the conductor, with positive values pointing away from the conductor and negative values pointing towards it. The expression -r cot theta tells us that the direction of the magnetic field is opposite to the direction of the z-axis, which aligns with the direction of the current flow in the conductor. This is known as the right-hand rule, where the thumb points in the direction of the current and the fingers curl in the direction of the magnetic field. Therefore, the negative sign is necessary to properly describe the direction of the magnetic field in relation to the z-axis and the current flow in the conductor.