Work out how long a model monorail will take to accelerate to 10 m/s with a magnetic flux field of 2T?
Answer:
The way the question is worded leads me to assume that the TOTAL length of wire in the magnetic field is 2cm, not that each turn is 2cm in the magnetic field so the number of turns is not important in the question...
First you must work out the force on the train using the equation:
F = B I L sin@
since @ = 90 the sin@ = 1
F=BIL where:
F is the force in Newtons
B is the magnetic field strength in Tesla
I is the current in Amperes
L is the total length of the conductor in the field in metres
so
F = 2 x 100 x 0.02 = 4N
now use newton's second law:
F = ma
a = F/m
a = 4/1 = 4m/s^2
acceleration is the change is speed per change in time and assuming the train starts from rest, the initial speed will be zero
a = (v - u)/t
where u is the initial speed in m/s
4 = (10 - 0) / t
t = 10/ 4 = 2.5s
Please note that magnetic flux is different from magnetic field.
Magnetic flux is the number of field lines and is measured in Webers (Wb)
1 Wb = 1x10^8 magnetic field lines
What we call magnetic field is actually magnetic flux density and is in Teslas. One Tesla is one Weber per square metre so it's how much area the field lines occupy if you like.
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