29.6
Magnetic Force Between Two Parallel Currents
Two long, straight, and parallel current-carrying conductors exert a force of equal magnitude on one another. The direction of the force depends on th…
Consider two infinitely long, parallel conductors carrying current in the same direction.
The force exerted by the magnetic field due to the first conductor, over a finite length of the second conductor, is given by the current multiplied by the vector product of the length vector and the field due to the first conductor.
The magnetic field is perpendicular to the length vector. Substituting the expression for magnetic field, the magnitude of the force on the second conductor is obtained.
According to the right-hand rule for the cross-product, the force on the second conductor points toward the first conductor.
Similarly, it can be shown that the field due to the second conductor exerts an equal magnitude of the force on the first conductor. However, the direction of this force is toward the second conductor.
Thus, for current flowing in the same direction, the magnetic field created around each conductor exerts an attractive force on the other.
If the current direction is reversed in either one of the conductors, there would be a repulsive force between the conductors.
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Q1: How does the direction of current affect the force between parallel conductors?
When currents flow in the same direction, the magnetic field created by each conductor exerts an attractive force on the other. If the current direction is reversed in either conductor, the force becomes repulsive. The force direction is determined by applying the right-hand rule to the cross-product of the length vector and magnetic field.
Q2: What is the mathematical expression for the force between two parallel current-carrying conductors?
The force exerted by the magnetic field of the first conductor on a finite length of the second conductor equals the current in the second conductor multiplied by the vector product of the length vector and the magnetic field. This cross-product relationship yields the force magnitude and direction between the conductors.
Q3: Why is the Ampere unit defined using parallel current-carrying conductors?
One Ampere is defined as the current in each of two parallel, infinitely long conductors separated by one meter in empty space that produces a force of exactly 1 Newton per meter between them. This definition uses the measurable force between parallel conductors as a fundamental standard for current measurement.
Q4: What is the pinch effect and where does it occur?
The pinch effect occurs when the attractive magnetic force between parallel currents squeezes current into a smaller tube. It appears in electric arcs and plasmas where charges move parallel to one another. In circuit breakers and solar plasma, this effect can concentrate arcs, burn holes in equipment, or shape solar flares and jets of ionized material.
Q5: How does the right-hand rule determine the direction of force on a current-carrying conductor?
The right-hand rule for the cross-product determines force direction by pointing your fingers along the length vector, curling them toward the magnetic field direction, and extending your thumb perpendicular to both. This thumb direction indicates the force on the conductor carrying current in the magnetic field.
Q6: Why does Coulomb repulsion not dominate the magnetic force between parallel currents?
The magnetic attraction between parallel currents is apparent when the overall charge density is zero. In this condition, Coulomb repulsion does not overwhelm the magnetic attraction. When charge density is not zero, electrostatic repulsion becomes dominant and masks the magnetic force effects.
Q7: What does force per unit length represent in the context of parallel conductors?
Force per unit length expresses the magnetic force between very long parallel conductors as force divided by conductor length. This normalized measurement simplifies calculations and comparisons, forming the basis for defining the Ampere unit and analyzing effects like the pinch effect in extended current-carrying systems.