Kendriya Vidyalaya Karwar

Physics Project

Class XII A By: Atit Gaonkar

Force Due To Parallel Current

Carrying Conductor

P

TOPIC• Force Due To Parallel

Current Carrying Conductor

• When a current-carrying conductor is placed in an external magnetic field B, the magnetic force on the conductor is given by:

• F = I (L x B)

• F = I L B sin θ

Force Due To Magnetic Field

Let L1 & L2 be two current carrying conductors, carrying current I1 & I2 separated by a distance ‘a’ producing magnetic field B1 & B2 respectively

• Consider two parallel wires of equal length carrying a steady current:

The two wires will exert magnetic forces on each other.

Wire 1 will exert a magnetic force on wire 2, wire 2 will exert a magnetic force on wire 1.

• From Amperean Law we know that the magnetic fields B1 & B2 :

• B1 = (μ◦* I1)/ 2Πa

• B2 = (μ◦* I2)/ 2Πa

• The wires are separated by distance ‘a’ and carry currents I1 and I2 in the same direction.

• Wire 2, carrying current I2, sets up a magnetic field B2 at the position of wire 1.

• The direction of the magnetic field B2 is known by using Right Hand Thumb Rule and the direction is perpendicular to the wire

• Therefore F21 = I1 (L x B2)

• As Angle Between L And B2 is 90

• So F21 = I1 L B2

• Therefore the force F21 = I1 L (μ◦ I2) / 2Πa

• Rewriting the force per unit length :

• F/L = I1 (μ◦ I2)/ 2Πa

• So, let F/L = F’

• F’ = I1 (μ◦ I2) / 2Πa

• F’ = (μ◦ I1 I2 ) / 2Πa

• The direction of F1 is towards the other conductor and is determined by using the right hand rule (fingers of right hand in direction of current I; palm facing in the direction of B; thumb points in the direction of Force)

• As the new force is directly proportional to I1 & I2 so the new force of wire1 and wire2 over each other will be same.

• The magnetic force that wire 1 exerts on wire 2 (F1 on 2) is equal in magnitude to and opposite in direction to F1 (F2 on 1).

• Wire 1 and wire 2 will attract each other.

• Note: Parallel conductors carrying currents in the same direction attract each other & parallel conductors carrying currents in opposite directions repel each other.

• So,

Parallel wires with current flowing in the same direction, attract each other.

Parallel wires with current flowing in the opposite direction, repel each other.

• Therefore

• Vector F21 = - Vector F12

• But | F21 | = | F12 |

• Therefore F’ = (μ◦ I1 I2 ) / 2Πa

• When I1 = I2 = I Ampere , a = 1m , then F’ = 2 * 10-7 N/m

• So,

• 1 Ampere can be defined as “When two current carrying conductors placed at a separation of 1m, and if they experiences a force of 2 * 10-7 N/m, then the current through the conductors are said to be 1 Ampere.