Magnetic field and wire current

[dmsgo89]

Homework Statement

A long, straight wire with linear mass density of 45g/m is suspended by threads, as shown in the figure . There is a uniform magnetic field pointing vertically downward. A 7.0A current in the wire experiences a horizontal magnetic force that deflects it to an equilibrium angle of 10 degree. What is the strength of the magnetic field B?

Homework Equations

B=(U_o I) / (2 *3.14 * r)

The Attempt at a Solution

I have U_0 given, I given. but can't find r.

How can find r to get B?

 

[kuruman]

The equation that you have quoted gives the magnetic field produced by a very long wire. It is not relevant here. What equation do you know that gives the force on a current-carrying wire segment in a magnetic field?

 

[dmsgo89]

F=ILB maybe?

 

[Winzer]

That's the right equation.
The next step is to draw a free body diagram and balance the forces.

 

[rdl]

I would suggest using the equation B=(U_o I) / (2 *3.14 * r) to solve for the unknown variable, r. This equation relates the magnetic field strength (B) to the permeability of free space (U_o), the current (I), and the distance between the wire and the magnetic field (r). In this case, the wire is suspended by threads, so the distance r would be the length of the wire. Therefore, you can rearrange the equation to solve for r by multiplying both sides by (2 *3.14 * r) and then dividing by (U_o I). This will give you the value of r, which you can then use to calculate the strength of the magnetic field B.