What is the Radial Distance for a Magnetic Field at a 45° Angle in a Solenoid?

[11thHeaven]

Homework Statement

A long solenoid with 10 turns per cm and a radius of 7 cm carries a current of 20mA. A current of 6 A flows in a straight conductor located along the central axis of the solenoid.

Homework Equations

(a) At what radial distance from the axis will the direction of the resulting magnetic field be at 45° to the axial direction?

The Attempt at a Solution

I really don't know where to start here. The only two equations our lecturer has spoken of are B=(u₀I)/(2∏r) for the magnetic field around a conducting wire, and B=Nu₀I for the magnetic field strength around a solenoid. I can work out the magnetic field strength due to each, but no idea where to start finding out what the "direction" of the resulting magnetic field will be.

Help appreciated! :)

 

[tiny-tim]

hi 11thHeaven!

A long solenoid with 10 turns per cm and a radius of 7 cm carries a current of 20mA. A current of 6 A flows in a straight conductor located along the central axis of the solenoid.
…
At what radial distance from the axis will the direction of the resulting magnetic field be at 45° to the axial direction?
…
I can work out the magnetic field strength due to each, but no idea where to start finding out what the "direction" of the resulting magnetic field will be.

45° means that the axial field and the tangential field must be equal in magnitude

 

[11thHeaven]

hi 11thHeaven!


45° means that the axial field and the tangential field must be equal in magnitude

I'm not entirely sure what is meant by the axial field and the tangential field; could you explain?

 

[tiny-tim]

the field along the axis, and the field that goes in circles round the axis

 

[Basic_Physics]

The magnetic field is a vector field. This means that one need to measure its components in 3 directions in order to construct it at any point. The axial measurements give the component along the (z) axis of the solenoid and the tangential measurements will give the other 2 components (x and y) mutually perpendicular to the axial direction. The resultant field in the solenoid will be the vector sum of the two fields, the circular field of the conductor and the axial field of the solenoid.

 

[11thHeaven]

the field along the axis, and the field that goes in circles round the axis

Great, thanks a lot