Sebuah elektron bergerak lurus sejajar dengan kawat dan searah dengan arah arus, dengan laju \( 5 \times 10^{4} \mathrm{~m} / \mathrm{s} \). Bila jarak elektron ke kawat 16 mm , maka besar dan arah gaya magnetik yang dialami elektron besarnya adalah (..... N mendekati/menjauhi kawat) a. \( 4.10^{-19} \mathrm{~N} \) menjauhi kawat b. \( 4.10^{-19} \mathrm{~N} \) mendekati kawat c. \( 2.10^{-19} \mathrm{~N} \) menjauhi kawat d. \( 2.10^{-19} \mathrm{~N} \) mendekati kawat e. \( 10^{-19} \mathrm{~N} \) menjauhi kawat

To solve the problem, we need to calculate the magnetic force experienced by the electron due to the current in the wire. The magnetic force \( F \) on a charged particle moving in a magnetic field is given by the formula: \[ F = q \cdot v \cdot B \cdot \sin(\theta) \] Where: - \( F \) is the magnetic force, - \( q \) is the charge of the electron, - \( v \) is the velocity of the electron, - \( B \) is the magnetic field strength, - \( \theta \) is the angle between the velocity vector and the magnetic field vector. ### Step 1: Identify known values - Charge of the electron, \( q = -1.6 \times 10^{-19} \, \text{C} \) - Velocity of the electron, \( v = 5 \times 10^{4} \, \text{m/s} \) - Distance from the wire, \( r = 16 \, \text{mm} = 0.016 \, \text{m} \) ### Step 2: Calculate the magnetic field \( B \) due to the wire The magnetic field \( B \) at a distance \( r \) from a long straight wire carrying a current \( I \) is given by: \[ B = \frac{\mu_0 I}{2 \pi r} \] Where: - \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \) (permeability of free space) However, we need the current \( I \) to calculate \( B \). Since it is not provided, we will keep it as a variable for now. ### Step 3: Calculate the force \( F \) Substituting \( B \) into the force equation, we have: \[ F = q \cdot v \cdot \left(\frac{\mu_0 I}{2 \pi r}\right) \cdot \sin(\theta) \] Assuming the electron moves parallel to the wire, \( \theta = 90^\circ \) and \( \sin(90^\circ) = 1 \): \[ F = q \cdot v \cdot \frac{\mu_0 I}{2 \pi r} \] ### Step 4: Substitute known values Now we can substitute the known values into the equation: \[ F = (-1.6 \times 10^{-19}) \cdot (5 \times 10^{4}) \cdot \frac{(4\pi \times 10^{-7}) I}{2 \pi (0.016)} \] This simplifies to: \[ F = (-1.6 \times 10^{-19}) \cdot (5 \times 10^{4}) \cdot \frac{(2 \times 10^{-7}) I}{0.016} \] Calculating the constant part: \[ F = (-1.6 \times 10^{-19}) \cdot (5 \times 10^{4}) \cdot (1.25 \times 10^{-5}) I \] Calculating the numerical part: \[ F = -1.6 \times 5 \times 1.25 \times 10^{-19} \times 10^{4} \times 10^{-5} I \] \[ F = -1 \times 10^{-19} I \] ### Step 5: Determine the direction of the force The direction of the force can be determined using the right-hand rule. Since the electron has a negative charge, the force will be in the opposite direction of what the right-hand rule indicates. If the current in the wire is flowing in the positive direction, the magnetic field will circle around the wire, and the force on the electron will be directed towards the wire. ### Conclusion The magnitude of the force depends on the current \( I \). However, since we are looking for the options provided, we can conclude that the force is directed towards the wire. Thus, the answer is: **b. \( 4.10^{-19} \mathrm{~N} \) mendekati kawat**