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  • (a) Define SI unit of current in terms of the force between two parallel current carrying conductors. (b) Two long straight parallel conductors carrying steady currents Ia and Ib along the same direction are separated by

(a) Define SI unit of current in terms of the force between two parallel current carrying conductors.

(b) Two long straight parallel conductors carrying steady currents Ia and Ib along the same direction are separated by a distance d. How does one explain the force of attraction between them? If a third conductor carrying a current Ic in the
opposite direction is placed just in the middle of these conductors, find the resultant force acting on the third conductor.

 

 
 
 
 
 

Answers (1)

The S.I unit of current is ampere.

The magnitude of force per unit length of two parallel current-carrying conductors.

F=\frac{\mu_{0}I_{a} I_{b}}{2\pi d}

Ampere is that value of steady-state current, which when maintained in each of the very two long, straight, parallel conductors of negligible cross-section and placed 1m apart in a vacuum produces 2\times 10^{-7}\; N/m force on each conductor. 

(b)

The magnetic field is into the plane of wire B 

so the direction of the force on wire B due to the current in wire A is towards A. 

similarly, the force on wire A due to current in B is towards B.

Therefore, the two wires attract each other 

       

Force on wire 3 due to 1 ;

F_{1}=\frac{\mu _{0}I_{a}I_{c}}{2\pi \frac{d}{2}}=\frac{\mu _{0}I_{a}I_{c}}{\pi d} towards the right

Force on wire 3 due to 2

F_{2}=\frac{\mu _{0}I_{b}I_{c}}{\pi d}    towards left

Net force

 F=F_{1}-F_{2}=\frac{\mu _{0}I_{a}I_{c}}{\pi d}-\frac{\mu _{0}I_{b}I_{c}}{\pi d}

                    =\frac{\mu _{0}I_{c}}{\pi d}(I_{a}-I_{b})  to the right.

Posted by

Safeer PP

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