A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35m x 0.55m. The magnetic field has a
magnitude of 2.1T and is inclined at an angle of 65 degrees with respect to the normal to the plane of the loops. (a) If the magnetic field decreases to zero in a time of 0.45s, what is the magnitude of the average emf induced in the loop.(b) If the magnetic field remains constant at its initail calue of 2.1T, what is the magnitude of the rate ΔA/Δt at which the area should change so that the average emf has the same magnitude as in part (a)?
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To solve this problem it is necessary to apply the concepts related to the frequency in a spring, the conservation of energy and the total mechanical energy in the body (kinetic or potential as the case may be)
PART A) By definition the frequency in a spring is given by the equation
Where,
m = mass
k = spring constant
Our values are,
k=1700N/m
m=5.3 kg
Replacing,
PART B) To solve this section it is necessary to apply the concepts related to the conservation of energy both potential (simple harmonic) and kinetic in the spring.
Where,
k = Spring constant
m = mass
y = Vertical compression
v = Velocity
This expression is equivalent to,
Our values are given as,
k=1700 N/m
V=1.70 m/s
y=0.045m
m=5.3 kg
Replacing we have,
Solving for A,
PART C) Finally, the total mechanical energy is given by the equation