A student thrusts a 0,20T magnet with a cross sectional area of 2.0 cm^2 into a coil of 400 turns in 0,50s. The coil has a resistance of 30 ohms and it is connected in series with a moving coil meter having a resistantace of 170 ohms. What is the average velocity and the current?
Figure the induced voltage (Faradays law)
EMf=N *B*A/time
Then divide this induced EMF by total resistance to get current.
http://physics.bu.edu/~duffy/PY106/InducedEMF.html
EMF = BLV i don't have the length but im trying to find the velocity?
go back to my formula. It is the basis for yours.
To find the average velocity and current, we need to use the formula and steps below:
1. Calculating the average velocity:
Average velocity (v) can be calculated using the formula:
v = Δx / Δt
In this case, the change in position (Δx) is the cross-sectional area of the magnet (2.0 cm^2) and the change in time (Δt) is given as 0.50 seconds.
Substituting the values into the formula:
v = 2.0 cm^2 / 0.50 s
Since the units are not consistent, we need to convert the units. 1 cm^2 is equal to (1 x 10^-4) m^2.
So, v = (2.0 x 10^-4) m^2 / 0.50 s
Calculating the value:
v = 4.0 x 10^-4 m^2 / s
Therefore, the average velocity is 4.0 x 10^-4 m^2 / s.
2. Calculating the current:
To calculate the current, we need to use Ohm's Law, which states:
I = V / R
Here, V is the voltage and R is the resistance.
The total resistance (RT) is the sum of the resistance of the coil (30 ohms) and the resistance of the moving coil meter (170 ohms).
So, RT = 30 ohms + 170 ohms = 200 ohms.
The voltage (V) can be calculated using Faraday's Law of Electromagnetic Induction:
V = N * ΔA / Δt
Here, N is the number of turns in the coil (400 turns), ΔA is the change in magnetic flux, and Δt is the change in time (0.50 seconds).
The change in magnetic flux (ΔΦ) can be calculated using the formula:
ΔΦ = B * A
Here, B is the magnetic field (0.20 T) and A is the cross-sectional area of the magnet (2.0 cm^2).
Substituting the values:
ΔΦ = 0.20 T * 2.0 cm^2
Since the units are not consistent, we need to convert the units. 1 T equals (1 x 10^4) gauss, and 1 cm^2 is equal to (1 x 10^-4) m^2.
So, ΔΦ = (0.20 T * 2.0 cm^2) * (1 x 10^4 gauss / 1 T) * (1 x 10^-4 m^2 / 1 cm^2)
Calculating the value:
ΔΦ = (0.20 T * 2.0 cm^2 * 1 x 10^4 gauss * 1 x 10^-4 m^2) / (1 T * 1 cm^2)
Simplifying the units and values:
ΔΦ = 4.0 x 10^-5 Wb (webers)
Now, substituting the values into the formula for voltage:
V = 400 turns * 4.0 x 10^-5 Wb / 0.50 s
Calculating the value:
V = 8.0 x 10^-3 V (volts)
Finally, calculating the current using Ohm's Law:
I = 8.0 x 10^-3 V / 200 ohms
Calculating the value:
I = 4.0 x 10^-5 A (amperes)
Therefore, the current is 4.0 x 10^-5 A.