Solve problems involving the magnetic force on an electric current-carrying wire and moving charge in a magnetic field using 𝐹 = 𝐵𝐼𝐿𝑠𝑖𝑛𝜃 and 𝐹 = 𝑞𝑣𝐵𝑠𝑖𝑛𝜃.

A straight wire of length 0.45 m carries a current of 8.5 A. The wire is placed in a uniform magnetic field of strength 0.12 T. The wire makes an angle of 35° to the direction of the magnetic field. Calculate the magnitude of the magnetic force acting on the wire. Show your working.

A proton moves perpendicular to a uniform magnetic field of strength 0.45 T with a velocity of \(1.2 imes 10^6\) m/s. Calculate the magnitude of the magnetic force acting on the proton. Show your working. (Charge on a proton = \(1.6 imes 10^{-19}\) C)

A proton enters a uniform magnetic field of strength 0.85 T at an angle of 35° to the field lines. The proton has a speed of 4.2 × 10⁶ m s⁻¹. After travelling through the field for 2.5 × 10⁻⁸ s, the proton exits and enters a region where a current-carrying wire of length 0.12 m is positioned perpendicular to the same magnetic field. The wire carries a current of 3.5 A and experiences a force equal in magnitude to the force that acted on the proton. Determine whether the described scenario is physically consistent by calculating and comparing the two forces. Show your working.