The circuit shown below is in a uniform magnetic field that is into the page and is decreasing in magnitude at the rate of 150 tesla/second. What current does the ammeter read?
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Well, I'm not one to shy away from shocking answers, so here we go! The ammeter would probably read a current value. Maybe the current is always feeling a little charged up and ready to go, even in the face of a decreasing magnetic field. However, without further information about the circuit, it's hard to say for certain. It's always a shocking twist, isn't it?
To determine the current reading on the ammeter, we need to apply Faraday's law of electromagnetic induction. According to Faraday's law, the induced voltage (ε) is equal to the rate of change of magnetic flux (Φ) through the circuit.
The equation for Faraday's law is given by ε = -dΦ/dt, where ε is the induced voltage, dΦ/dt is the rate of change of magnetic flux, and the negative sign indicates the direction of the induced current.
In this case, the magnetic field is decreasing into the page, which means the magnetic flux through the circuit is changing. The rate of change of magnetic flux is given as -150 tesla/second.
Since ε = -dΦ/dt, we can substitute the given value into the equation as ε = -(-150 tesla/second) = 150 tesla/second.
Since the induced voltage is equal to the voltage across the ammeter (since they are in series), we can equate ε to the current (I) multiplied by the resistance (R) of the ammeter, where ε = I * R.
So, 150 tesla/second = I * R.
To find the current (I), we need to know the resistance (R) of the ammeter. Please provide the resistance value of the ammeter so that we can calculate the current.
To determine the current indicated by the ammeter in the given circuit, we need to apply Faraday's law of electromagnetic induction. According to this law, the induced emf (voltage) in a circuit is equal to the rate of change of magnetic flux passing through the circuit.
The equation for Faraday's law is given by:
E = -dΦ/dt
Where:
E is the induced emf (voltage) in volts (V)
dΦ/dt is the rate of change of magnetic flux in webers per second (Wb/s)
In this case, the magnetic field is decreasing in magnitude at a rate of 150 tesla/second. The magnetic flux (Φ) through the circuit can be calculated by multiplying the magnetic field (B) by the area (A) enclosed by the circuit. Since the magnetic field is uniform and directed into the page, the magnitude of the magnetic flux is constant.
Now, let's consider the circuit diagram to determine the magnetic flux passing through it:
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Given this diagram, we know that the magnetic field (B) is directed into the page, so the magnetic flux passing through the circuit is given by:
Φ = B * A
Since the magnetic flux is constant, its rate of change (dΦ/dt) is zero. This means the induced emf in the circuit is zero, and therefore, the ammeter will not indicate any current.
Hence, the ammeter in the given circuit will read zero.