Magnetic Force

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As for a particle in motion p = mv

To determine the magnetic field inside a solenoid, we use the following formula: where: is the permeability of free space ( ), is the number of turns per unit length, is the current flowing through the solenoid. Step 1: Understanding (Turns per Unit Length) The number of turns per unit length is defined as: where: is the total number of turns in the solenoid, is the length of the solenoid. Step 2: Substituting into the Magnetic Field Formula By substituting into the magnetic field formula, we get: Conclusion: The magnetic field inside a solenoid is directly proportional to the current and the number of turns per unit length . Therefore, the correct expression for the magnetic field is: Final Answer:

The magnetic force on a charged particle moving in a magnetic field is given by the Lorentz force formula: Where: - (charge of the proton), - (velocity of the proton), - is the magnetic field due to the current-carrying wire, - is the angle between the velocity of the proton and the magnetic field. Since the proton moves parallel to the wire and the current, the magnetic field produced by the wire is perpendicular to the velocity of the proton. Thus, , and . First, calculate the magnetic field at a distance from the wire using the formula for the magnetic field due to a long straight current-carrying wire: Where: - , - , - . Substitute the values: Now, calculate the magnetic force: Thus, the magnitude of the magnetic force acting on the proton is .

The magnetic force on a moving charge is given by the formula: Where: - , - , - , - . Substitute the values: Thus, the magnetic force is .

The magnetic force on a charged particle moving in a magnetic field is given by: Where: - (charge of electron), - (speed of electron), - (magnetic field), - (angle between velocity and magnetic field). Substituting the values: Since , we get: Thus, the magnitude of the magnetic force on the electron is N.