Example:
A plane of wingspan 30m flies through a vertical field of strength 5 x 10-4T. Calculate the emf induced across wing tips if its velocity = 150ms-1.
Answer:
Calculate the area swept out each second by the wings. Multiply that by the field strength, B and you have got the flux swept out in a second.
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i don't understand this lil piece but they found the area by
Area= 30m *150m/s = 4500 m2
How does this work? wouldn't the untis be m2/s (which isn't area)?
Where did that assupmtion or eqn come frm?
EMF is change in (B*A) per second. Since B is constant, EMF is B * deltaArea/time
The units for change in area /time is m^2/sec
In this example, the area mentioned is the area swept out by the wings in one second. The equation used to calculate the area is:
Area = wingspan * velocity = 30m * 150m/s = 4500m^2.
The units of this area are indeed square meters (m^2). The calculation does not involve dividing by time, so the units are not m^2/s.
To understand why we use this equation, let's consider the situation. As the plane moves through the magnetic field, the wings cut through the field lines, resulting in a change in magnetic flux. The magnitude of the change in flux depends on both the strength of the magnetic field and the area that is swept out in a given time.
By multiplying the wingspan by the velocity, we are essentially calculating the area that is swept out by the wings per unit time. This is the effective area over which the magnetic field lines pass through.
So, in summary, the equation used to calculate the area represents the area swept out by the wings in one second, and the units are in square meters (m^2). It is used to determine the change in magnetic flux, which is a factor in calculating the induced emf in the plane's wings.