The uniform wire is bent into the shape shown and held by...

Name: The uniform wire is bent into the shape shown and held by the frictionless pin at O. Determine the angle θ (0 ≤θ≤ 180^∘) which will allow the wire to hang in the orientation shown. Assume a = 1.6r, b = 1.9r.
Uploaded: 2019-05-31T07:07:19-08:00
Duration: 5 min 44 s
Channel: Jayashree Behera
Description: The uniform wire is bent into the shape shown and held by the frictionless pin at O. Determine the angle θ (0 ≤θ≤ 180^∘) which will allow the wire to hang in the orientation shown. Assume a = 1.6r, b = 1.9r.

The uniform wire is bent into the shape shown and held by the frictionless pin at O. Determine the angle $\theta$ ($0 \le \theta \le 180^\circ$) which will allow the wire to hang in the orientation shown. Assume $a = 1.6r$, $b = 1.9r$.

Transcript

00:01 The force is accepted by the magnetic field is given by i .e.

00:07 Times l cross b.

00:09 And so the magnitude of force is going to be i .l .b.

00:13 Times sine 5, where phi is the angle between l and b.

00:18 And the direction of f is given by right -hand rule being applied on the length of the direction of the flow of current and the magnetic field direction.

00:30 For the wire to remain at rest, the net force on the wire should be zero.

00:36 That is, the force exerted on it on the wire by the magnetic field must have a component directed up the incline.

00:45 So like that.

00:47 So there should be a component of magnetic field along this direction.

00:52 Now to produce a force in this direction, the current on the wire must be directed from left, from right to left.

01:01 In the figure with the problem in the textbook or viewing the wire from its left hand end from the left hand in the direction should be as shown over here so this is the image of the wire from its left hand end and so we have a magnetic field a component of magnetic field upward so that there is a component of magnetic field along the direction of incline and forces here and so current must be directed from left to right so sorry from right to left so that is that should be like this so current going from this angle the current should be coming out of the plane of the screen so we draw the free body diagram of this for the wire.

02:09 So this is the free body diagram that i have already drawn.

02:16 So basically y is the direction of the incline upward and x is perpendicular to that and x points positive x is downward...

Question

The uniform wire is bent into the shape shown and held by the frictionless pin at O. Determine the angle $\theta$ ($0 \le \theta \le 180^\circ$) which will allow the wire to hang in the orientation shown. Assume $a = 1.6r$, $b = 1.9r$.

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