Finding the Magnetic force on the coil

[Physicslearner500039]

Homework Statement

A voice coil in a loudspeaker has 50 turns of wire and a diameter of 1.56 cm, and the current in the coil is 0.950 A. Assume that the magnetic field at each point of the coil has a constant magnitude of 0.220 T and is directed at an angle of 60.0 Deg outward from the normal to the plane of the coil. Let the axis of the coil be in the y-direction. The current in the coil is in the direction shown (counterclockwise as viewed from a point above the coil on the y-axis). Calculate the magnitude and direction of the net magnetic force on the coil.

Relevant Equations

F=ILBSin(Θ)

Surely a tough one, I am doing it from the basics. This is the diagram i tried to draw showing the Force and current I

The Length L is the tangent to the circle. The Force F is pointing upwards at $90 Deg$ to the $\vec B$ and also perpendicular to $\vec L$. I am considering a small length $\vec dL = r d\theta$. Resolving the force into X and Y components and integrating over the complete $2\pi$.

$Fx = \int_0^{2\pi} IRB\sin(30) d\theta$
$Fy = \int_0^{2\pi} IRB\cos(30)d\theta$

Is my approach correct or completely wrong? Please advise

 

[TSny]

Check the direction of F in your drawing. The current is going into the page at the point where you draw F.

If you consider the forces on diametrically opposite elements of current, what happens when you add their horizontal components?

Your integral for $F_y$ looks good except for maybe the overall sign. If $\theta$ varies from 0 to $2 \pi$, how many times do you go around the cylinder?

 

[Physicslearner500039]

Check the direction of F in your drawing. The current is going into the page at the point where you draw F.

I am not sure how i have done that mistake, the updated diagram is

The horizontal components cancel out. The vertical component is for N turns
$-\int_0^{2\pi} NIRB\cos(30)d\theta$
$-\pi NIRB\sqrt3 = -0.443 \hat j N$

 

[TSny]

Looks right to me.