Examples 437 



7. A current i flows round a circle of radius a, and a current i' flows in a very long 

 straight wire in the same plane. Shew that the mutual attraction is 47m'' (sec a 1), where 

 a is the angle subtended by the circle at the nearest point of the straight wire. 



8. If, in the last question, the circle is placed perpendicular to the straight wire with 

 its centre at distance c from it, shew that there is a couple tending to set the two wires in 

 the same plane, of moment 2im'a 2 /e or 27m 'c, according as c> or < a. 



9. A long straight current intersects at right angles a diameter of a circular current, 

 arid the plane of the circle makes an acute angle a with the plane through this diameter 

 and the straight current. Shew that the coefficient of mutual induction is 



47T {c sec a (c 2 sec 2 a - a 2 )^} or 4?rc tan (-7 5 



according as the straight current passes within or without the circle, a being the radius of 

 the circle, and c the distance of the straight current from its centre. 



10. Prove that the coefficient of mutual induction between a pair of infinitely long 

 straight wires and a circular one of radius a in the same plane and with its centre at a 

 distance b(>a) from each of the straight wires, is 



11. A circuit contains a straight wire of length 2 conveying a current. A second 

 straight wire, infinite in both directions, makes an angle a with the first, and their 

 common perpendicular is of length c and meets the first wire in its middle point. Prove 

 that the additional electromagnetic forces on the first straight wire, due to the presence 

 of a current in the second wire, is a wrench of pitch 



_ / . , a sin a\ I . , . a sin a 



2 a sin a c tan ~ J - / sin 2a tan ~ * . 

 V c )l c 



12. Two circular wires of radii a, b have a common centre, and are free to turn on an 

 insulating axis which is a diameter of both. Shew that when the wires carry currents 

 i, i\ a couple of magnitude 



is required to hold them with their planes at right angles, it being assumed that b/a is so 

 small that its fifth power may be neglected. 



13. Two circular circuits are in planes at right angles to the line joining their centres. 

 Shew that the coefficient of induction 



where a, c are the longest and shortest lines which can be drawn from one circuit to the 

 other. Find the force between the circuits. 



14. Two currents i, i' flow round two squares each of side a, placed with their edges 

 parallel .to one another and at right angles to the distance c between their centres. Shew 

 that they attract with a force 



2 + C 2 "w 



