Answer the following question:Be sure to show all work. Include formulae and units.Be sure to include relavant, meaningful diagram and a complete circuit diagram with circuit related problem. take enough space, don't try to squeeze everything on a small space!(problems are from:principle of physics:calculus based; Chapter:current and direct current circuits and Magnetic forces - Magnetic field)

Q.n.1) A 50-volt battery is connected by a long straight wire to a 100 W resistor and 12,500 µF capacitor in series. If the capacitor is initially uncharged, what will be the magnitude of the magnetic field 1 mm from the wire two seconds after the circuit is connected?

Cannot be answered, unless you assume the max current produces 100W. When choosing resistors, that is an unwise decision.

But assuming the unwise choice, the resistance of the resistor is
P=v^2/R
R= 50^2/100=25 ohm

current initial= 2 amps

I(t)=2e^(-T/RC)

than find magnetic field from the current.

To find the magnitude of the magnetic field 1 mm from the wire two seconds after the circuit is connected, we need to use the formula for the magnetic field produced by a long straight wire.

The formula for the magnetic field produced by a long straight wire is given by:

B = (μ₀ * I) / (2π * r)

Where:
B = Magnetic field (in Teslas)
μ₀ = Permeability of free space (constant value of 4π x 10^-7 T m/A)
I = Current flowing through the wire (in Amperes)
r = Distance from the wire (in meters)

To determine the current flowing through the circuit, we can use Ohm's Law. Ohm's Law states that the current flowing through a conductor is equal to the voltage across the conductor divided by its resistance:

I = V / R

Where:
I = Current (in Amperes)
V = Voltage (in Volts)
R = Resistance (in Ohms)

Given:
Voltage (V) = 50 Volts
Resistance (R) = 100 Ohms

Substituting the values into Ohm's Law, we can find the current flowing through the circuit:

I = 50 V / 100 Ω
I = 0.5 A

Now that we have the current flowing through the wire (I), and we want to find the magnetic field 1 mm from the wire (r = 0.001 m), we can substitute these values into the formula for the magnetic field:

B = (4π * 10^-7 Tm/A * 0.5 A) / (2π * 0.001 m)
B = (2 * 10^-7 T) / (0.002 m)
B = 10^-7 T / (0.001 m)
B = 10^-4 T

Therefore, the magnitude of the magnetic field 1 mm from the wire two seconds after the circuit is connected is 10^-4 Tesla.