A wire that is 0.86 meters long is moved perpendicularly through a constant magnetic field of strength 0.035 newtons/amp·meter at a speed of 6.0 meters/second. What is the emf produced?
area swept out: .86x6*timeinseconds
or 5.16m^2/sec
E=BdA/dt=.035*.86*6 volts
To calculate the emf (electromotive force) produced in a wire moving through a magnetic field, you can use Faraday's law of electromagnetic induction. According to this law, the emf induced in a wire is directly proportional to the rate at which the magnetic flux through the wire changes.
In this case, the wire is moved perpendicularly through a constant magnetic field. To calculate the emf produced, you need to determine the rate of change of magnetic flux.
The formula for calculating the emf is:
emf = B * L * v
Where:
- emf is the electromotive force (volts),
- B is the magnetic field strength (tesla),
- L is the length of the wire (meters),
- v is the velocity of the wire (meters/second).
Given values:
- B = 0.035 newtons/amp·meter (converted to tesla),
- L = 0.86 meters,
- v = 6.0 meters/second.
First, convert the units:
- 1 newton/amp·meter = 1 tesla. So, B remains as 0.035 tesla.
Now, plug in the values into the formula:
emf = (0.035 tesla) * (0.86 meters) * (6.0 meters/second)
Calculating this expression gives:
emf ≈ 0.1794 volts
Therefore, the emf produced in the wire is approximately 0.1794 volts.