With a magnetic field of 3.0 mT at the center of a 0.60 diameter loop, what is the current in the loop?
Wouldn't it matter how many turns? There is a formula for this...
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c2
To find the current in the loop, you can use Ampere's law, which states that the magnetic field at the center of a loop is directly proportional to the current passing through the loop. The formula for Ampere's law is given as:
B = (μ₀ * I) / (2π * r)
Where:
- B is the magnetic field at the center of the loop
- μ₀ is the permeability of free space (a constant value of 4π × 10⁻⁷ T·m/A)
- I is the current flowing through the loop
- r is the radius of the loop
In this case, the diameter of the loop is given (0.60 m), so we can calculate the radius (r) by dividing the diameter by 2:
r = 0.60 m / 2 = 0.30 m
Plugging in the values into the formula, we can rearrange it to solve for the current (I):
B = (μ₀ * I) / (2π * r)
I = (B * 2π * r) / μ₀
Now, substitute the given values:
B = 3.0 mT (convert to tesla: 3.0 × 10⁻³ T)
r = 0.30 m
μ₀ = 4π × 10⁻⁷ T·m/A
I = (3.0 × 10⁻³ T * 2π * 0.30 m) / (4π × 10⁻⁷ T·m/A)
Now, simplify and solve for I:
I = (1.8 × 10⁻² T·m/A) / (4π × 10⁻⁷ T·m/A)
I = 4.5 × 10⁴ A
Therefore, the current in the loop is 4.5 × 10⁴ A (amperes).