## Step 1: Calculate the Magnitude of the Velocity The magnetic force on a moving charge is given by: \[ F = |q|vB \] where \( F = .360 \, \text{N} \)force to the left), \(q| =6.00, \mutext{C = 6.00 \times10^{-6} \, \{C}), \( B = 6.00 \, \text{T} \). Solve for \( v \): \[ v = \frac{F}{|q|B} \] \[ v = \frac{.360}{6.00 \times 10^{-6} \times 6.00} \] \[ v = \frac{.360}{36. \times 10^{-6}} \] \[ v = \frac{.360}{3.6 \times 10^{-5}} \] \[ v = 1.00 \times 10^4 \, \text{m/s} \] **Explanation:** We used the formula for the force on a charged particle moving perpendicular to a magnetic field to solve for the speed. --- ## Step 2: Determine the Direction of the Velocity - The force is to the left (negative x-direction). - The charge is **negative** (\( q < \)). - The magnetic field is **downward** (negative y-direction). Use the right-hand rule for \( \vec{F} = q\vec{v} \times \vec{B} \): - For a positive charge, \( \vec{v} \) would be **out of the page** to cause a leftward force. - Since the charge is negative, the direction is **reversed**, so \( \vec{v} \) must be **into the page**. **Explanation:** The negative charge reverses the direction predicted by the right-hand rule; thus, velocity is into the page. --- ## Final Answer \[ \boxed{1.00 \times 10^4 \, \text{m/s} \text{ into the page}} \] **(b) is correct.**

# Velocity Calculation of a Charged Particle in a Magnetic Field ## Step 1: Calculate the Magnitude of the Velocity The magnetic force acting on a moving charge is described by the equation: \[ F = |q|vB \] Where: - \( F = 0.360 \, \text{N} \) (force directed to the left), - \( |q| = 6.00 \, \mu C = 6.00 \times 10^{-6} \, C \), - \( B = 6.00 \, \text{T} \). To find the velocity \( v \), rearrange the formula: \[ v = \frac{F}{|q|B} \] Substituting in the values: \[ v = \frac{0.360}{6.00 \times 10^{-6} \times 6.00} \] Calculating the denominator: \[ 6.00 \times 10^{-6} \times 6.00 = 36.00 \times 10^{-6} \] Now calculating \( v \): \[ v = \frac{0.360}{36.00 \times 10^{-6}} = \frac{0.360}{3.6 \times 10^{-5}} = 1.00 \times 10^4 \, \text{m/s} \] **Explanation:** We derived the velocity from the magnetic force equation, confirming the calculations show that the magnitude of the velocity is \( 1.00 \times 10^4 \, \text{m/s} \). --- ## Step 2: Determine the Direction of the Velocity To establish the direction of the velocity \( \vec{v} \): - The magnetic force \( \vec{F} \) is to the left (negative x-direction). - The charge \( q \) is negative (\( -6.00 \, \mu C \)). - The magnetic field \( \vec{B} \) is directed downward (negative y-direction). Using the right-hand rule (\( \vec{F} = q\vec{v} \times \vec{B} \)): - For a positive charge, the velocity \( \vec{v} \) would point **out of the page** to generate a force to the left. - Since the charge is negative, we invert the direction. Therefore, \( \vec{v} \) must be directed **into the page**. **Explanation:** The presence of a negative charge changes the expected direction of velocity as predicted by the right-hand rule, leading to a final direction of velocity that is into the page. --- ## Final Answer \[ \boxed{1.00 \times 10^4 \, \text{m/s} \text{ into the page}} \] The correct answer is (b) \( 1.00 \times 10^4 \, \text{m/s} \) into the page.