A long straight current-carrying wire is supported by light strings tied to the

Question

A long straight current-carrying wire is supported by light strings tied to the wire at regular intervals. The figure shows a cross-sectional view-in this view, the current in the wire is directed perpendicular to the page. The wire, which is horizontal, hangs at equilibrium so that the strings make a 30° angle from the vertical. The wire is in a uniform magnetic field directed down-the magnetic field has a magnitude of 0.350 T. The wire has a mass per unit length of 0.190 kg/m. We will define out of the page to be the positive direction, so you can use a positive sign in your answer below if the current is out of the page, and a negative sign if the current is into the page. What is the magnitude and direction of the current in the wire? ing 30 current-carrying wire

Explanation / Answer

Clearly the magnetic force is in right hand side, hence from Fleming's left hand rule we can say that current is directed outwards from the screen, that is in positive direction.

Taking component of tension and comparing with forces ( weight which is downwards and magnetic force which is in right hand side direction), we get

Tcos(30)=mg {wieght of wire}

Tsin(30) = iBl { magnetic force}

Dividing both equations

tan(30) =iBl / mg

Given, B=0.35 T, m/l=0.19 kg/m ,

Putting all values we get,

i= 3.071 amperes

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