A 36 cm long copper wire carries a current of 6.0 A and weighs 0.45 N. A certain magnetic field is strong enough to balance the force of gravity on the wire. What is the strength of the magnetic field?

To find the strength of the magnetic field, we can use the formula for the force experienced by a current-carrying wire in a magnetic field:

F = BIL

where F is the force, B is the magnetic field strength, I is the current, and L is the length of the wire.

In this case, we are given the length of the wire (L = 36 cm = 0.36 m), the current (I = 6.0 A), and the weight of the wire (0.45 N). The force experienced by the wire due to gravity is equal to its weight, so:

F_gravity = m * g

where m is the mass of the wire and g is the acceleration due to gravity (9.8 m/s²). The weight can be calculated using the formula:

weight = mass * acceleration due to gravity

Since weight is given as 0.45 N, we can find the mass of the wire:

m = weight / g

Now, let's calculate the mass:

m = 0.45 N / 9.8 m/s²

m ≈ 0.046 kg

Now we have the values needed to calculate the magnetic field strength:

F = BIL

B = F / (IL)

B = (0.45 N) / (0.046 kg × 6.0 A × 0.36 m)

B ≈ 3.30 T

Therefore, the strength of the magnetic field is approximately 3.30 Tesla (T).