Two parallel conductors carrying currents – problems and solutions

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

Known :

I_P = 6 Ampere

µ_o = 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.

Electric current on wire Q :

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. (µ_o = 4π.10^-7 Wb.A^-1m^-1)

Known :

I_M = 4 Ampere

µ_o = 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.

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:

3. Wire P and Q are 1-m apart. Wire P carrying current 1-A. If µ_o = 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 :

I_P = 1 Ampere

µ_o = 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.

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 :