A long wire carries a current of 1 ampere.Find the magnitude of the magnetic field 2 meter away from the wire.
B=μ₀•I/2πa= 4π•10⁻⁷‧1/2•π•2 =10⁻⁷ T
Well, if this wire were a person, it would've definitely earned the title of "Mr. Ampere" for carrying a current of 1 ampere. But, instead, it chose the path of being a wire. Such a waste of talent!
Anyway, let's calculate the magnitude of the magnetic field 2 meters away from this "electrically inclined" wire. To do so, we can use Ampere's law (how fitting!) and a bit of geometry.
So, assuming we have an infinitely long straight wire (a wire that goes on and on, just like my jokes), we find that the magnetic field around it is given by the equation B = (μ0 * I) / (2 * π * r).
Where:
- B is the magnetic field strength,
- μ0 is the permeability of free space (which is 4π * 10^-7 T m/A, but I'll spare you the complicated math here),
- I is the current flowing through the wire, and
- r is the distance from the wire.
Now, plugging in the values, we get B = (4π * 10^-7 T m/A * 1 A) / (2 * π * 2 m).
After doing some quick calculations, we find that the magnitude of the magnetic field 2 meters away from the wire is approximately 1.26 × 10^-6 Tesla.
So, the wire might be lacking in its career choice, but at least it can give us a handy magnetic field to work with. Don't you just love the wonders of science?
To find the magnitude of the magnetic field produced by a long wire carrying a current, you can use Ampere's Law.
Ampere's Law states that the magnetic field around a closed loop is directly proportional to the current enclosed by the loop.
The formula to calculate the magnetic field produced by a long wire at a distance r is given by:
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 distance from the wire
Using the given values, we can calculate the magnetic field:
B = (4π × 10⁻⁷ T·m/A * 1 A) / (2π * 2 m)
B = (4π × 10⁻⁷) / (4π)
B = 10⁻⁷ T
Therefore, the magnitude of the magnetic field 2 meters away from the wire is 10⁻⁷ Tesla.
To find the magnitude of the magnetic field created by a long wire carrying a current, you can use Ampere's Law. Ampere's Law relates the magnetic field (B) to the current (I) and the distance (r) from the wire.
The equation is given as:
B = (μ0 * I) / (2π * r)
Where:
B is the magnetic field,
I is the current,
r is the distance from the wire, and
μ0 is the permeability of free space, which is a constant with a value of 4π * 10^-7 T·m/A.
In this case, the current (I) is 1 Ampere and the distance (r) is 2 meters.
Plugging in these values into the equation, we get:
B = (4π * 10^-7 * 1) / (2π * 2)
= (4π * 10^-7) / (4π)
= 10^-7 T
Therefore, the magnitude of the magnetic field 2 meters away from the wire is 10^-7 Tesla (T).