Prof. David R. Jackson ECE Dept. Spring 2015 Notes 33 ECE 2317 Applied Electricity and Magnetism 1

Force on Wire Single charge: Wire: q B v F The contour C is in the direction of the reference direction for the current. B I F C 2 (derivation omitted)

Example Note: There is no self-force on wire 2 due to the magnetic field produced by the current on wire 2. Find the force F 2 on wire 2 3 Note: The contour C 2 runs from point A to point B, defined by the current reference direction on wire 2. I2I2 I1I1 1 2 z h z = 0 z = L x C2C2 y A B

Example (cont.) 4 F 1 = - F 2 F2F2 A B I1I1 I2I2 z x z = L Note: The contour C 2 runs from z = 0 to z = L (since I 2 runs in this direction).

Definition of Amp Assume F1F1 F2F2 A B I I z x Definition of Amp: Note:

Definition of Amp (cont.) (an exact constant) 6 Force per unit length: so:

Example 7 F1F1 F2F2 A B I I z x 2 1 (attractive force) In a power substation, the current in two parallel buses is 1 [ kA ]. The buses are 1 [ m ] apart. What is the force per unit length between the two buses?

Example (cont.) 8 Note: 1 [kG]  9.8 [N] = 2.2 [lbs] or

Example 9 During a lighting strike, the current in two parallel wires reaches 10 [ kA ]. The wires are 1 [ cm ] apart. What is the force per unit length between the two wires? (attractive force) F1F1 F2F2 A B I I z x 2 1

Example (cont.) 10 or Note: 1 [kG]  9.8 [N] = 2.2 [lbs]

Example 11 In a DC motor, the armature consists of N = 10,000 turns (loops) of wire, with each turn being L = 0.1 [ m ] in length (in the direction parallel to the axis). The magnetic flux density produced by the stator is B = 0.5 [ T ]. The radius of the armature is R = 0.05 [ m ]. Find the torque on the armature. The current through the motor is 3 [ A ]. Assume that the magnetic field is constant and perpendicular to the wire current. Note: There is no net force on the entire loop, since the force from opposite sides cancels. Both sides (left ad right) of the loop contribute equally to the torque. Axis of rotation

Example (cont.) 12 Therefore, we have Axis of rotation or

Torque on Current Loop 13 A planar current loop of wire carries a current I as shown below. B = magnetic flux density vector (assumed constant here). Define magnetic dipole moment of loop: Torque vector on loop:

DC Motor 14 A loop rotating in a DC magnetic field is shown below. rr N N S N N S A commutator is needed to reverse the current every 180 o and make the torque in same direction.

DC Motor (cont.) 15 The commutator reverses the current every 180 o. Note: The rings are positioned so that the torque changes sign (current reverses) at the point where the torque is zero. Commutator (rings) Brushes

DC Motor (cont.) 16 In practice, there are multiple loops and commutator segments. The torque is thus more constant as the armature turns. Commutator in a universal motor from a vacuum cleaner. Parts: (A) commutator, (B) brush, (C) rotor (armature) windings, (D) stator (field) windings, (E) brush guides