Two parallel wires, separated by the distance of 2 cm, carry the currents I1 = 1 A and I2 = 2 A in the same direction. How far from the wire carrying the current I1 is the magnetic field zero?
I am wondering if the answer might be that it can never equal 0. Since the current is traveling in the same direction B2-B1=0 in between the wires.
between wires
field is down from one of them and up from the other
The B from a wire times 2 pi * distance from the wire is proportional to the current through
so
1/2pir = 2/ 2pi(2 -r)
2 r = 2 - r
3 r = 2
r = .66666666667 cm
:)
To determine at what distance from the wire carrying the current I1 the magnetic field becomes zero, we can use the concept of magnetic fields produced by current-carrying wires.
The magnetic field produced by a long straight wire is given by Ampere's law, which states that the magnetic field (B) at a distance (r) from the wire is directly proportional to the current (I) and inversely proportional to the distance:
B = (μ0 * I) / (2 * π * r)
where μ0 is the permeability of free space (μ0 ≈ 4π × 10^-7 T·m/A).
In the given scenario, we have two parallel wires carrying currents I1 = 1 A and I2 = 2 A in the same direction and separated by a distance of 2 cm.
To find the distance from the wire carrying current I1 where the magnetic field becomes zero, we need to determine at what point the magnetic fields produced by the two wires cancel each other out.
Let's consider a point P located at some distance x from the wire carrying current I1. At this point P, the magnetic field due to the wire carrying current I1 (B1) and the magnetic field due to the wire carrying current I2 (B2) add up.
B1 = (μ0 * I1) / (2 * π * x)
B2 = (μ0 * I2) / (2 * π * (2 cm - x))
Since the currents are in the same direction, the magnetic fields add up algebraically:
B = B1 + B2
Setting B equal to zero, we can solve for x:
0 = B1 + B2
0 = (μ0 * I1) / (2 * π * x) + (μ0 * I2) / (2 * π * (2 cm - x))
Solving this equation will give us the value of x at which the magnetic field becomes zero.
However, upon solving the equation, we find that x can never be zero or negative. The magnetic field between the wires will not become exactly zero. This is because, as you correctly pointed out, the currents in the wires are in the same direction, resulting in a non-zero magnetic field in between the wires.
So, in this particular scenario, there is no point between the wires where the magnetic field becomes exactly zero.