A long, straight wire carrying a current of 317 A is placed in a uniform magnetic field that has a magnitude of 7.69 × 10-3 T. The wire is perpendicular to the field. Find a point in space where the net magnetic field is zero. Locate this point by specifying its perpendicular distance from the wire.
I=317 A
B=7.69•10⁻³ T
B(wire)=B
B(wire)=μ₀I/2πa =B
a= μ₀I/2πB=
=4π•10⁻⁷•317/2π•7.69•10⁻³=8.24•10⁻³ m
Clarification to Elena's Answer:
B(wire)=(4π•10⁻⁷•317)/(2π•7.69•10⁻³)=8.24•10⁻³ m
To find the point in space where the net magnetic field is zero, we can use the equation for the magnetic field produced by a current-carrying wire:
B = (μ₀ * I) / (2π * r)
Where:
B is the magnetic field
μ₀ is the permeability of free space (4π × 10^-7 T m/A)
I is the current
r is the perpendicular distance from the wire
Since the wire is perpendicular to the field, we know that the magnetic field due to the wire will only have a component along the perpendicular distance from the wire (r direction).
At the point where the net magnetic field is zero, the field due to the wire must cancel out the magnetic field in the uniform magnetic field.
Let's set up the equation using the given values:
7.69 × 10^-3 T = (μ₀ * 317 A) / (2π * r)
Now, we can solve for r:
r = (μ₀ * 317 A) / (2π * 7.69 × 10^-3 T)
Plugging in the values:
r = (4π × 10^-7 T m/A * 317 A) / (2π * 7.69 × 10^-3 T)
Simplifying:
r = 2.06 m
Therefore, the point in space where the net magnetic field is zero is located at a perpendicular distance of 2.06 meters from the wire.