Final answer:
The magnitude of the current in the circuit is 2.35 amperes, found using Ohm's Law. The magnitude of the force on a wire within a magnetic field is calculated as 0.12 newtons using the formula F = ICB sin θ and applying the right-hand rule to determine its direction.
Step-by-step explanation:
To find the magnitude of the current in the circuit, we utilize Ohm's Law, which is given as V = IR, where V is the voltage, I is the current, and R is the resistance. In the provided information, the total voltage V is 12.0 volts, and the total resistance Rtot is 5.11 ohms. By rearranging Ohm's Law to solve for I, we get I = V / R. Substituting the given values, we calculate I = 12.0 V / 5.11 Ω = 2.35 A. Thus, the magnitude of the current flowing through the circuit is 2.35 amperes (A).
Next, we apply the equation F = ICB sin θ to find the magnitude of the force on a wire due to the magnetic field. With the current I = 1.5 A, the length of the wire L = 0.040 m, the magnetic field B = 2.0 T, and the angle θ = 90°, the force exerted on the wire is calculated as F = (1.5 A) × (0.040 m) × (2.0 T) = 0.12 N. To find the direction of the force, the right-hand rule is used: point your fingers in the direction of the current (I), curl them towards the magnetic field (B), and your thumb will point in the direction of the force, which in this case is the x-direction.