Questions: Homework 2 Begin Date: 9/2/2024 11:59:00 PM Due Date: 9/10/2024 11:55:00 PM End Date: 9/10/2024 11:55:00 PM Problem 3: (13% of Assignment Value) A uniform electric field of magnitude 19.6 N / C is parallel to the x axis. A circular loop of radius 24.7 cm is centered at the origin with the normal to the loop pointing 37.4° above the x axis. Part (a) Calculate the electric flux in, newton squared meters per coulomb, through the loop. Φ= N · m^2 / C

Solution Steps

• Electric field magnitude, \( E = 19.6 \, \text{N/C} \)
• Radius of the loop, \( R = 24.7 \, \text{cm} = 0.247 \, \text{m} \)
• Angle between the normal to the loop and the electric field, \( \theta = 37.4^\circ \)

The area \( A \) of a circular loop is given by: \[ A = \pi R^2 \] \[ A = \pi (0.247 \, \text{m})^2 \] \[ A \approx 0.1917 \, \text{m}^2 \]

The electric flux \( \Phi \) through the loop is given by: \[ \Phi = E \cdot A \cdot \cos(\theta) \] \[ \Phi = 19.6 \, \text{N/C} \cdot 0.1917 \, \text{m}^2 \cdot \cos(37.4^\circ) \] \[ \cos(37.4^\circ) \approx 0.796 \] \[ \Phi \approx 19.6 \cdot 0.1917 \cdot 0.796 \] \[ \Phi \approx 2.99 \, \text{N} \cdot \text{m}^2/\text{C} \]

Final Answer