1.
A rectangular coil 0.065 m by 0.080 m is positioned
so that its cross-sectional area is perpendicular
to the direction of a magnetic field.
The coil has 66 turns and a total resistance of
7.6 Ω and the field decreases at a rate of 2.5
T/s.
What is the magnitude of the induced current
in the coil?
Answer in units of A.
2.
A student attempts to make a simple generator by passing a single loop of wire between the poles of a horseshoe magnet with a magnetic field of 2.0 ×10−2 T. The area of the loop is 4.87 ×10−3 m2 and is moved perpendicular to the magnetic field lines.
In what time interval will the student have
to move the loop out of the magnetic field in
order to induce an EMF of 1.9 V?
Answer in units of s.
3.
A student attempts to make a simple generator
by wrapping a long piece of wire across
a cylinder with a cross-sectional area of 1.076×10−3 m2. She then passes the coil betweenthe poles of a horseshoe magnet with a magnetic field of 2.2 ×10−2 T. The student finds that by removing the coil perpendicular to the magnetic field lines during 0.29 s, a voltage drop of 145 mV can be induced across the wire.
How many turns of wire are wrapped
around the coil?
4.
A bolt of lightning, such as the one shown on
the left in the figure, behaves like a vertical
wire conducting electric current. As a result,
it produces a magnetic field whose strength
varies with the distance from the lightning. A
139-turn circular coil with a radius of 0.842
m is oriented perpendicular to the magnetic
field as shown. The magnetic field at the coil
drops from 4.99×10−3 T to 0.00 T in 10.7 µs.
What is the average emf induced in the
coil?
Answer in units of V.
I have almost finished my homework just these questions left. I really need help.
I'd be happy to help you with your remaining questions! Let's work through them one by one.
1. To find the magnitude of the induced current in the coil, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf (electromotive force) in a loop of wire is equal to the rate of change of magnetic flux through the loop. The emf can be calculated using the formula:
emf = -N * (dΦ/dt)
Where:
emf = induced emf (in volts)
N = number of turns in the coil
dΦ/dt = rate of change of magnetic flux (in webers per second)
In this case, the rate of change of magnetic flux is given as 2.5 T/s, and the number of turns in the coil is 66. Therefore, we can calculate the induced emf as follows:
emf = -66 * (2.5 T/s)
Next, we need to find the magnitude of the induced current in the coil. We can use Ohm's law, which states that the current flowing through a coil is equal to the induced emf divided by the total resistance of the coil. In this case, the total resistance of the coil is given as 7.6 Ω. Therefore, we can calculate the current as follows:
current = emf / total resistance
current = emf / 7.6 Ω
Finally, we can substitute the value of the emf from the earlier calculation to find the magnitude of the induced current in the coil.
2. To determine the time interval required to induce an EMF of 1.9 V, we can use Faraday's law of electromagnetic induction again. In this case, we're given the area of the loop (4.87 × 10^(-3) m^2) and the magnetic field (2.0 × 10^(-2) T). We can calculate the rate of change of magnetic flux (dΦ/dt) using the formula:
dΦ/dt = B * A * v
Where:
B = magnetic field (in teslas)
A = area of the loop (in square meters)
v = velocity of the loop (in meters per second)
We want to find the time interval (t), so we rearrange the formula to solve for t:
t = ΔΦ / (-dΦ/dt)
Where:
ΔΦ = change in magnetic flux (in webers) = EMF induced (in volts)
Now we can substitute the given values to find the time interval required:
t = 1.9 V / (-dΦ/dt)
t = 1.9 V / (-(B * A * v))
Remember to use the negative sign because the induced EMF opposes the change in magnetic flux.
3. To determine the number of turns of wire wrapped around the coil, we can use the formula for calculating the induced voltage:
voltage = -N * dΦ/dt
Given that voltage is 145 mV (or 0.145 V), the change in magnetic flux (dΦ/dt) is 2.2 × 10^(-2) T, and the time interval (t) is 0.29 s, we can rearrange the formula to solve for N:
N = voltage / (-dΦ/dt * t)
Substitute the given values to find the number of turns of wire wrapped around the coil.
4. To find the average emf induced in the coil, we can use Faraday's law once again. The average emf (E_avg) can be calculated using the formula:
E_avg = (-ΔΦ / Δt) * N
Where:
ΔΦ = change in magnetic flux (in webers)
Δt = change in time (in seconds)
N = number of turns in the coil
In this case, we're given the change in magnetic field (from 4.99 × 10^(-3) T to 0.00 T) and the change in time (10.7 µs, or 10.7 × 10^(-6) s). The number of turns in the coil is given as 139. Substitute these values into the formula to find the average emf induced in the coil.
Remember to pay attention to the units and convert them if necessary to ensure consistency in your calculations. Let me know if you have any further questions or need assistance with the calculations!