An infinitely long wire carries a current of three amps. The magnetic field outside the wire:
A. points radially away from the wire
B. points radially inward
C. circles the wire
D. is zero.
The correct answer and explanation is:
The correct answer is C. circles the wire.
In the case of an infinitely long straight current-carrying wire, the magnetic field generated by the current forms concentric circles around the wire. This is explained by Ampère’s Law, which relates the magnetic field around a current-carrying conductor to the current flowing through it. The law states that the line integral of the magnetic field around a closed loop is proportional to the enclosed current.
For a straight, infinitely long wire, the magnetic field at any point outside the wire is tangential to a circle centered on the wire. The direction of the magnetic field can be determined using the right-hand rule. If you curl the fingers of your right hand in the direction of the current, your thumb will point along the direction of the magnetic field. This rule shows that the magnetic field forms a circular pattern around the wire.
The strength of the magnetic field decreases with distance from the wire, and it is directly proportional to the current. The magnitude of the magnetic field at a distance rr from the wire can be given by the equation: B=μ0I2πrB = \frac{\mu_0 I}{2 \pi r}
where:
- BB is the magnetic field strength,
- μ0\mu_0 is the permeability of free space (4π×10−7 T\cdotpm/A4 \pi \times 10^{-7} \, \text{T·m/A}),
- II is the current (in this case, 3 A),
- rr is the radial distance from the wire.
Thus, the magnetic field is non-zero outside the wire and it forms circular loops around it, with the field’s direction depending on the direction of the current and the position relative to the wire.