Direction of Magnetic Field Outside a Cylindrical Wire

[Cazicami]

Hi guys, sorry to bug again, but I am a wee bit stuck.

Homework Statement

A steady current of 1A flows down an infinitely long straight cylindrical wire of radius r=5mm

Explain in what direction the magnetic field is pointing outside the wire

Homework Equations

The Biot Savart law - B = 4∏/μ ∫∫∫ ((Jdv) x r)/r²

Sorry for the poor equation

The Attempt at a Solution

I would have said the magnetic field would point radially around the wire.

However the solutions say: From the Biot-Savart law follows that the magnetic field has to point in azimuthal direction. The radial component is zero.

I have tried googling azimuthal as I have no idea what it means, and it seems to mean an angle away from horizontal, but if anyone could clear up what the answer is, or direct me to something that would help that would be great.

Thanks

 

[TSny]

For a point p located a distance r from the wire, imagine a circle of radius r lying in a plane perpendicular to the wire, with center at the wire, and passing through the point p. "Azimuthal" means tangent to the circle.

 

[Cazicami]

Thanks, but why is the field tangential to that point and not radial around the loop?

 

[TSny]

Think about the direction of the cross product $\vec{J}\times\hat{r}$ in your integral expression for the Biot-Savart law.

[Minor comment: When you wrote the integral for the Biot-Savart law, the fraction out front should be $\frac{\mu_o}{4\pi}$]

 

[m1rohit]

you should use right hand thumb rule while calculating cross products.In this case you can also work with pointing your right thumb along the direction of the current then the way your fingers curl to form a fist is the direction of the field.clock wise concentric circles from top.