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 equation that relates the force experienced by a current-carrying wire in a magnetic field to the current, length of the wire, and strength of the magnetic field.
The formula is:
F = BIL
Where:
F is the force experienced by the wire (which can be balanced by the force of gravity),
B is the strength of the magnetic field,
I is the current flowing through the wire,
and L is the length of the wire.
In this case, we know the current (I = 6.0 A), the length of the wire (L = 36 cm = 0.36 m), and the force experienced by the wire (F = 0.45 N). We want to find the strength of the magnetic field (B).
Rearranging the formula, we get:
B = F / (IL)
Plugging in the known values:
B = 0.45 N / (6.0 A × 0.36 m)
Simplifying:
B = 0.45 N / 2.16 Am
Calculating:
B = 0.2083 T
Therefore, the strength of the magnetic field is 0.2083 Tesla.