Two long parallel wires separated by a distance, d, carry currents in opposite directions. If the left-hand wire carries a current i/2, and the right-hand wires carries a current i, determine where the magnetic field is zero.
What if both the wires are carrying the same current then the magnetic field where would be zero
It will not be a point between the wires, because the fields of both wides are in the same direction there.
The field will be zero at a distance d away from the wire carrying the smaller current, on the opposite side from the other wire.
That is because the ratio of current to distance from the wire wuth that current will be the same for both wires, and the field directions will be opposite, thereby canceling.
two long parallel wires carrying currents i1 and i2 in opposite directions. What are the magnitude and direction of the net magnetic field at point P? Assume the following values: i1= 10 A, i2= 20 A, and d = 5 cm
Two long, straight, parallel wires conduct currents of 4 A and 10 A
in opposite directions. If a 2 m-length of one of the wires experiences
a force of magnitude 2 × 10−3 N, calculate the distance between
the wires.
To determine where the magnetic field is zero, we can use Ampere's Law. Ampere's Law states that the integral of the magnetic field along a closed loop is equal to the product of the current enclosed by the loop and the permeability of free space.
Let's consider a rectangular loop that is parallel to the wires, with its longer sides perpendicular to the wires. The length of the loop is L, and the width is w. We will place the loop such that one wire is on the left of the loop and the other wire is on the right of the loop.
Now, let's calculate the magnetic field due to each wire separately and then determine where their contributions cancel out.
1. Magnetic field due to the left-hand wire:
The integral of the magnetic field along the loop will be B1 * L (top side) - B1 * L (bottom side) = 0, because the magnetic field is zero inside the wire.
2. Magnetic field due to the right-hand wire:
The integral of the magnetic field along the loop will be B2 * L + B2 * L = 2B2 * L, as the magnetic field is constant along the length of the loop. Here, B2 represents the magnetic field due to the right-hand wire.
According to Ampere's Law, this value should be equal to the product of the current enclosed by the loop and the permeability of free space. Since the current enclosed by the loop is i/2 + i = (3/2)i, we have:
2B2 * L = (3/2)i * μ₀
B2 = (3/4π) * (i / L) * μ₀
Now, for the magnetic field to be zero, B1 must equal B2. However, we already found that B1 = 0, so B2 must also be zero. Therefore, we need to find the value of L for which B2 is zero.
Using the equation for B2 above, we set it to zero:
(3/4π) * (i / L) * μ₀ = 0
Since μ₀ is a constant and i is a non-zero value, in order for the equation to be satisfied, (i / L) must be zero. This means that L must be infinity.
Therefore, the magnetic field due to the wires is zero at an infinitely far distance from the wires.