Right hand rule finding direction of magnetic force

[JosephK]

Homework Statement

A strong magnet is placed under a horizontal conducting ring of radius r that carries current I as shown in the figure below. The magnetic field makes an angle θ with the vertical at the ring's location.

(b) What is the direction of the resultant magnetic force on the ring?

2
to the left
to the right
upward
downward
into the screen
out of the screen

Homework Equations

Right hand rule

The Attempt at a Solution

?

 

[SammyS]

What have you tried?

Where are you stuck?

 

[JosephK]

Crossing L and B from equation F = ILXB , where L is pointing in the same direction as current, magnetic force would point in a downward angle.

To point straight downwards the magnetic force, B has to point in a direction perpendicular to the current, although here it is pointing at an angle. So, is the B pointing not straight downwards but downwards at an angle?

 

[amy andrews]

Umm...remember that the force is always perpendicular to both the current and the magnetic field. In the right hand rule, your thumb is the force, pointing finger is the current, and your middle finger is the field.
What are you having trouble with?

 

[SammyS]

Consider any small piece, ΔL, of the ring, where the direction of ΔL is the same as the direction of the current, I. Using the right hand rule for the magnetic force, ΔF = IΔL×B, the direction of which is outward and downward at an angle of θ below the horizontal.

What is the result of summing ΔF over the whole ring?

 

[JosephK]

Umm...remember that the force is always perpendicular to both the current and the magnetic field. In the right hand rule, your thumb is the force, pointing finger is the current, and your middle finger is the field.
What are you having trouble with?

The curvy B field throws me off.

 

[SammyS]

At the points where the B field intersects the ring, B is at an angle θ from the vertical, pointing outward from the ring (as well as upward).

Consider two small pieces of the ring located directly opposite each other, (ΔL)₁ & (ΔL)₂. Now take the magnetic force on each and add these forces. The vertical components add (they're both downward) and the horizontal components cancel.

What does that tell you about the net magnetic force on the ring?

 

[JosephK]

The magnetic force is downward.

This is how I curl my fingers, correct?

 

[JosephK]

Would the magnetic force point inwards and downwards or outwards and downwards?

 

[SammyS]

OOPS ! I said: Outward & downward in post #5 & elsewhere. It should be inward & upward.

Post #8 does not show the right hand rule for the cross product of two vectors.

See the link in the above sentence. Also see the paragraph http://en.wikipedia.org/wiki/Right_...ssociated_with_an_ordered_pair_of_directions"

amy andrews also gives a (correct) version in Post #4, above.

 

[JosephK]

Thank you