Let's solve the problem step by step: --- ## **Step 1: Understand the Problem** - **Given:** Two point charges: \( +2q \) (left), \( +4q \) (right). - **Task:** Sketch the electric field lines for this setup, showing the overall field pattern. --- ## **Step 2: Principles of Electric Field Lines** - **Field lines start on positive charges** and go outward (since both are positive, lines radiate outward). - **Number of lines proportional to charge magnitude** (twice as many lines from \(+4q\) as from \(+2q\)). - **Lines never cross.** - **Field is stronger where lines are denser.** --- ## **Step 3: Sketching the Field Lines** ### **A. Assign Number of Field Lines** Let’s use: - \(+2q\) — 2 field lines per \(+q\) → **4 lines** from \(+2q\) - \(+4q\) — 2 field lines per \(+q\) → **8 lines** from \(+4q\) ### **B. Draw the Pattern** 1. **From Each Charge:** - Draw 4 lines radiating from \(+2q\). - Draw 8 lines radiating from \(+4q\). 2. **Direction:** - All lines point outward from both charges. - Some lines in the region **between the charges** will repel each other but will "bend away" from each other because both charges are positive. 3. **Relative Strength:** - The field is **stronger near \(+4q\)** (more lines closely spaced). - The lines leaving the region between the charges will bow outward due to repulsion. --- ## **Step 4: Sketch** Here's an ASCII-style description of the field lines (for visual reference): ``` / | \ / | \ / | \ / | \ +2q +4q \ | / \ | / \ | / \ | / ``` - **More lines go out from \(+4q\) than \(+2q\).** - **No lines connect the two charges directly** (since lines go out to infinity, not to another positive charge). - **Lines between the charges curve outward due to repulsion.** --- ## **Step 5: Explanation** - **Proportionality:** The number of lines represents the charge. - **Field Direction:** Outward for positive charges. - **No Connection:** No field lines from one charge to the other, since both are positive. --- ## **Final Answer:** ### **Electric Field Lines Sketch and Features** 1. Draw 4 lines radiating from \(+2q\), evenly spaced. 2. Draw 8 lines radiating from \(+4q\), evenly spaced. 3. The lines between the charges curve outward, showing repulsion. 4. The field is denser near \(+4q\), indicating a stronger field. 5. No lines connect the charges directly. --- ### **[Hand-drawn Sketch Example]** Here’s an illustrative sketch (you should draw something similar for your answer):  *Alt text: Electric field lines radiating outwards from two positive charges, with more lines from the larger charge (+4q) and lines bowing outward between them due to repulsion.* --- ### **Summary Table** | Charge | Number of Lines | Direction | Field Density | |---------|-----------------|-------------------|----------------| | +2q | 4 | Outward | Less dense | | +4q | 8 | Outward | More dense | --- **This completes the required sketch and explanation.**