Q#1072: [Electromagnetism > Force between current-carrying wires] (Past Exam Paper – June 2012 Paper 41 & 43 Q7)
Two long straight parallel copper wires A and B are clamped vertically. The wires pass through holes in a horizontal sheet of card PQRS, as shown in Fig. 7.1.
(a) There is a current in wire A in the direction shown on Fig. 7.1.
On Fig. 7.1, draw four field lines in the plane PQRS to represent the magnetic field due to the current in wire A.
(b) A direct current is now passed through wire B in the same direction as that in wire A. The current in wire B is larger than the current in wire A.
(i) On Fig. 7.1, draw an arrow in the plane PQRS to show the direction of the force on wire B due to the magnetic field produced by the current in wire A.
(ii) Wire A also experiences a force. State and explain which wire, if any, will experience the larger force.
(c) The direct currents in wires A and B are now replaced by sinusoidal alternating currents of equal peak values. The currents are in phase.
Describe the variation, if any, of the force experienced by wire B.
Solution 1072:
(a)
sketch: concentric circles (minimum of 3 circles)
separation increasing with distance from wire
correct direction
{The direction is obtained from the right hand grip rule.}
(b)
(i) arrow direction is from wire B towards wire A
{The direction of the force on wire B is obtained from Fleming’s left hand rule. Thumb = direction of force, forefinger = direction of magnetic field at wire B (this is towards SR, parallel to RQ) and middle finger = direction of current flowing in wire B (upwards).}
(ii)
EITHER reference to Newton’s third law
OR the force on each wire is proportional to the product of the two currents,
so the forces are equal
(c) The force is always towards wire A/ always in the same direction. It varies from zero (to a maximum value) {when the currents in both wires are zero}. The variation is sinusoidal / sin2 (at) twice frequency of current {since the force depends on the product of the 2 currents (which are sinusoidal and in phase)}
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