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Page 831: Lesson Check
On the other hand, the motor can’t be used without electricity. The motor converts the electrical power to mechanical work which can be used for moving some objects, lifting an object, grinding…
In general, the motor and the generator have a very similar construction, so we can say that the motor represents the generator that work’s in a reverse. $$
Principe of work is completely reverse, this is the main difference.
$$
begin{align}
varepsilon_{max}=Ncdot{B}cdot{A}cdotomega
end{align}
$$
Where the $N$ stands for the number of loops, $A$ stands for the area of each individual loop, $B$ represents the magnitude of the magnetic field and $omega$ is the angular speed.
The emf is directly proportional to an angular speed.
$$
boxed{text{If we increase the angular speed, the emf will also increase.}}
$$
$$
begin{align}
varepsilon_{max}=Ncdot{B}cdot{A}cdotomega
end{align}
$$
Where the $N$ stands for the number of loops, $A$ stands for the area of each individual loop, $B$ represents the magnitude of the magnetic field and $omega$ is the angular speed.
The emf is directly proportional to a number of loops.
$$
boxed{text{If we increase the coil loops number, the emf will also increase.}}
$$
$$
begin{align}
varepsilon_{max}=Ncdot{B}cdot{A}cdotomega
end{align}
$$
Where the $N$ stands for the number of loops, $A$ stands for the area of each individual loop, $B$ represents the magnitude of the magnetic field and $omega$ is the angular speed.
Let’s express the magnitude of the magnetic field from the first equation:
$$
begin{align*}
B&=frac{varepsilon_{max}}{Ncdot{A}cdotomega}
end{align*}
$$
If we substitute all given:
$$
begin{align*}
B&=frac{75text{ V}}{95cdot{0.0044text{ m}^2}cdot{220 frac{text{rad}}{text{s}}}}
end{align*}
$$
Now we just have to compute the value:
$$
boxed{B=0.816text{ T}}
$$
B=0.816text{ T}
$$
$$
begin{align}
varepsilon_{max}=Ncdot{B}cdot{A}cdotomega
end{align}
$$
Where the $N$ stands for the number of loops, $A$ stands for the area of each individual loop, $B$ represents the magnitude of the magnetic field and $omega$ is the angular speed.
Let’s substitute all given:
$$
begin{align*}
varepsilon_{max}=55cdot{0.95text{ T}}cdot{0.0085text{ m}^2}cdot{310 frac{text{rad}}{text{s}}}
end{align*}
$$
Now we just have to compute the value:
$$
boxed{varepsilon_{max}=137.7text{ V}}
$$
varepsilon_{max}=137.7text{ V}
$$
$$
begin{align}
varepsilon_{max}=Ncdot{B}cdot{A}cdotomega
end{align}
$$
Where the $N$ stands for the number of loops, $A$ stands for the area of each individual loop, $B$ represents the magnitude of the magnetic field and $omega$ is the angular speed.
Let’s express the area of the loop from the first equation:
$$
begin{align*}
A&=frac{varepsilon_{max}}{Ncdot{B}cdotomega}
end{align*}
$$
If we substitute all given:
$$
begin{align*}
A&=frac{22text{ V}}{27cdot{0.82text{ T}}cdot{290 frac{text{rad}}{text{s}}}}
end{align*}
$$
Now we just have to compute the value:
$$
boxed{A=0.00343text{ m}^2}
$$
A=0.00343text{ m}^2
$$