## (a) Ratio of Magnitudes (\(q_1/q_2\)) ### **Step 1: Count the Electric Field Lines** - The number of electric field lines is proportional to the magnitude of the charge. - From the image: - \(q_1\) (left, red): 8 field lines emanating. - \(q_2\) (right, gray): 4 field lines terminating. **Explanation:** Field lines start from positive charges and end on negative charges. The count represents the relative magnitudes. --- ### **Step 2: Calculate the Ratio** - Ratio of magnitudes: \[ \frac{|q_1|}{|q_2|} = \frac{\text{Number of lines from } q_1}{\text{Number of lines to } q_2} = \frac{8}{4} = 2 \] **Explanation:** The ratio is simply the ratio of field lines, assuming each line represents the same amount of charge. --- ### **Final Answer (a):** \[ \boxed{2} \] The magnitude of \(q_1\) is twice that of \(q_2\). --- ## (b) Sketch of Electric Field Lines Far from the Charges ### **Step 1: Analyze the System Far Away** - At a large distance, the two charges act like a single charge with net charge \(q_1 + q_2\). - Since \(q_1\) is positive and \(q_2\) is negative but smaller in magnitude, the net charge is positive. **Explanation:** Far from the charges, the field lines behave as if they are from a single charge equal to the algebraic sum. --- ### **Step 2: Draw the Field Lines** - Draw straight radial lines outward from a central point (representing a net positive charge). - The number of lines is proportional to \((q_1 - |q_2|)\). **Explanation:** The field will look like that of a single positive charge because the positive charge is larger. --- ### **Final Answer (b):** **The field lines far away will look like those of a single positive charge, spreading radially outward.** --- **Sketch Example:** ``` \ | / \ | / -- o -- / | \ / | \ ``` *(o = combined center, lines radiate outward)* --- Let me know if you need a digital sketch for part (b)!