Two parallel conductors carrying currents – problems and solutions

1. Wire P carrying current 6-A upward as shown in the figure below. If µo = 4π.10-7 wb A-1 m-1 and there is a repulsive force between wire P and Q 1.2.10-5 N.m1. Determine the magnitude and direction of electric current on wire Q.

Known :Two parallel conductors carrying currents – problems and solutions 1

IP = 6 Ampere

µo = 4π x 10-7 wb A-1 m-1

F/l = 1,2 x 10-5 N m-1

L = 1 meter

Wanted: Magnitude and direction of electric current on wire Q

Solution :

The direction of electric current on wire Q :

There is a repulsive force between wire P and Q so that the electric current on wire P has opposite direction with the electric current on wire Q.

On wire P, electric current upward so that on wire Q electric current downward.

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Electric current on wire Q :

Two parallel conductors carrying currents – problems and solutions 2

2. Two wires parallel, L, and M are 2-cm apart (see figure). Wire M carries a current of 4-A. Both wires exert a repulsive force on each other 6 x 10-5 Nm-1. Determine magnitude and direction of electric current on wire L. (µo = 4π.10-7 Wb.A-1m-1)

Known :Two parallel conductors carrying currents – problems and solutions 3

IM = 4 Ampere

µo = 4π x 10-7 wb A-1 m-1

F/l = 6 x 10-5 N m-1

L = 2 cm = 0.02 m

Wanted: Magnitude and direction of electric current on wire L

Solution :

The direction of the electric current on wire L :

There is a repulsive force between the wire L and the wire M so that the electric current on the wire L is in opposite direction with the current on the wire M.

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On the wire M electric current is directed upwards so that on the wire L the electric current is downward.

Electric current on wire L:

Two parallel conductors carrying currents – problems and solutions 4

3. Wire P and Q are 1-m apart. Wire P carrying current 1-A. If µo = 4π.10-7 Wb.A-1.m-1 and there is an attractive force on each other 10-7 N.m-1, determine magnitude and direction of electric current on wire Q.

Known :

IP = 1 AmpereTwo parallel conductors carrying currents – problems and solutions 5

µo = 4π x 10-7 wb A-1 m-1

F/l = 10-7 N m-1

L = 1 meter

Wanted: Magnitude and direction of current on wire Q

Solution :

The direction of electric current on wire Q :

There is an attractive force between wire P and wire Q so that the direction of the electric current on the wire P is the same as the direction of current on wire Q.

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On wire P the direction of electric current is downward so that on wire Q the direction of electric current is downward.

Electric current on wire Q :

Two parallel conductors carrying currents – problems and solutions 6

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