The circuit shown in the figure encloses an area of 25 cm2. The magnetic field increases steadily from 0 T to 0.50 T in 0.2 ms. What is the current in the resistor during this time?

The circuit has a 9.0 v battery and a 20 ohm resistor

To find the current in the resistor, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a closed loop is equal to the rate of change of magnetic flux through the loop.

The induced emf (ε) can be expressed as:

ε = -dΦ/dt

Where
ε = induced emf
Φ = magnetic flux
t = time

The magnetic flux (Φ) through the circuit can be calculated using the formula:

Φ = B * A

Where
B = magnetic field strength
A = area enclosed by the circuit

Given that the area (A) is 25 cm² = 0.0025 m² and the magnetic field increases from 0 T to 0.50 T in 0.2 ms = 0.0002 seconds, we can substitute these values into the formulas:

Initial Magnetic Flux (Φi) = B_initial * A = 0 T * 0.0025 m² = 0 Weber
Final Magnetic Flux (Φf) = B_final * A = 0.50 T * 0.0025 m² = 0.00125 Weber

The change in magnetic flux (ΔΦ) is then calculated by subtracting the initial flux from the final flux:

ΔΦ = Φf - Φi = 0.00125 Wb - 0 Wb = 0.00125 Wb

Since the change in magnetic flux is known, we can now calculate the induced emf (ε) using the equation mentioned earlier:

ε = -dΦ/dt

To find the current (I) in the resistor, we need to use Ohm's law, which states that the current (I) flowing through a resistor is equal to the voltage (V) across the resistor divided by its resistance (R):

I = V/R

Given that the battery voltage (V) is 9.0 V and the resistance (R) is 20 ohms, we can substitute these values into the formula:

I = 9.0 V / 20 Ω = 0.45 A

Therefore, the current in the resistor during the time when the magnetic field increases is approximately 0.45 Amperes.