Two long, parallel wires, each with a mass per unit length of 15 g/m, are supported in a horizontal plane by 6.0-cm-long strings, as shown in the figure below. Each wire carries the same current I, causing the wires to repel each other so that the angle ? between the supporting strings is 16°. (a) Are the currents in the same or opposite directions? (b) Determine the magnitude of each current. A
Given: The mass per unit length of the two parallel wire is 15 g/m.
The length of the string is 6 cm.
The angle between the supporting string is 16 degree.
To determine: The direction and magnitude of the current in each wire.
The magnitude of the force per unit length between the wire is given as
where I is the current and d is the distance between the wires.
When the wires are hanging with the help of the string, the magnetic force between the wire must be balancing the weight of each wire and the tensions in the string holding the wire up, therefore the magnetic force must be repulsive and the direction of current should be in opposite direction.
In equilibrium, the net force or the sum of the forces must be zero.
Note: The angle between the tension in the string and the vertical is half the angle between the supporting string,
The net force in the horizontal direction is
The net force in the vertical direction is
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