A straight 1.2 m length iron rod is moved at 10 m/s through the earth's magnetic field at a location where it has magnitude 1.0 × 105 T. What is the magnitude of the induced emf between one end of the wire and the other end?
What formula do I use?
Magnetic field of
the Earth is ≈ 10^-5 T (!!!)
ε = B•l•v =1•10^- 5•1.2•10 =1.2•10^-4
To calculate the magnitude of the induced electromotive force (emf) in a straight conductor moving through a magnetic field, you can use the formula:
emf = B * L * v
where:
- emf is the induced electromotive force (in volts)
- B is the magnitude of the magnetic field (in teslas)
- L is the length of the conductor (in meters)
- v is the velocity of the conductor perpendicular to the magnetic field (in meters per second)
In this case, the values given are:
- B = 1.0 × 10^5 T (magnitude of the magnetic field)
- L = 1.2 m (length of the iron rod)
- v = 10 m/s (velocity of the rod through the magnetic field)
Plugging these values into the formula, we have:
emf = (1.0 × 10^5 T) * (1.2 m) * (10 m/s)
Simplifying, we get:
emf = 1.2 × 10^6 V
Therefore, the magnitude of the induced emf between one end of the wire and the other end is 1.2 × 10^6 volts.
To determine the magnitude of the induced emf in a moving iron rod through a magnetic field, you can use the formula for electromagnetic induction:
Emf = Bvl
Where:
- Emf is the induced electromotive force or voltage (in volts, V)
- B is the magnetic field strength (in teslas, T)
- v is the velocity of the rod (in meters per second, m/s)
- l is the length of the rod (in meters, m)
In this case, the values are:
- B = 1.0 × 10^5 T (given in the question)
- v = 10 m/s (given in the question)
- l = 1.2 m (given in the question)
By substituting these values into the formula, we get:
Emf = (1.0 × 10^5 T) * (10 m/s) * (1.2 m)
Simplifying this expression gives:
Emf = 1.2 × 10^6 V
Therefore, the magnitude of the induced emf between one end of the wire and the other end is 1.2 × 10^6 volts.