# Step 1: Conceptual Questions (Parts 1 & 2) ## 1a. **Requirement on Electrical Charge** - **Explanation:** For molecules to move toward the anode, they must be **negatively charged**. This is because the anode is positively and attracts negative charges. Positively charged molecules would move toward the cathode instead. ## 1b. **Separation and Permittivity** - **Explanation:** The separation depends on the **relative permittivity (\(\epsilon_r\))** of the gel: - The electric field in the gel is \(E = V/(d \epsilon_r)\) (where \(V\) is voltage, \(d\) is distance). - A **higher permittivity** reduces the electric field, thus **slowing down separation**. ## 1c. **Increasing Voltage: Problems** - **Explanation:** Accelerating separation by increasing voltage can cause: - **Excessive heating** (Joule heating), risking gel melting or sample denaturation. - **Band distortion** due to uneven migration. - **Buffer breakdown** or electrolysis. ## 2. **Electric Field Sketch and Electrode Width** - **Explanation:** - **Inside the area between electrodes:** The electric field is mostly uniform and vertical (from cathode to anode). - **Outside the area:** The field lines curve outward due to edge effects. - **If electrodes are shorter than the gel width:** Edge effects become significant, leading to a **non-uniform field**. This causes **uneven separation**, with molecules near the edges migrating differently from those in the center. --- **Summary for Step 1:** - Molecules must be negatively charged to move toward the anode. - Higher gel permittivity slows separation. - Increasing voltage can cause overheating and distortion. - Short electrodes create non-uniform electric fields, harming separation accuracy. --- # Step 2: Electric Field Calculation (Part 3) ### **Given:** - Anode length (\(L\)) = 12 cm = .12 m - Charge distribution (\(\lambda\)) = .5 C/mm = 500 C/m - Distance between electrodes (\(d\)) = 18 cm = .18 m #### **We want:** The ratio: \[ \frac{E_{\text{center, anode}}}{E_{\text{center, cathode}}} \] #### **Electric Field from a Finite Line of Charge:** At a distance \(r\) perpendicular to the center of a line of length \(L\): \[ E = \frac{1}{4\pi\epsilon_} \cdot \frac{2\lambda L}{r \sqrt{L^2 + 4r^2}} \] - **At the center of the gel plate (midpoint between electrodes):** - Distance to anode: \(d = .18\) m Plug in the numbers (cathode not powered, so only anode field matters): \[ E_{\text{center}} = \frac{1}{4\pi\epsilon_} \frac{2 \lambda L}{d \sqrt{L^2 + 4d^2}} \] - **At the center of the cathode (i.e., directly above the anode, but at a distance):** - The field is much weaker due to geometry and distance. #### **Since the cathode is not powered, the field at the center of the cathode is almost zero**, so the field at the center of the gel (from the anode) is **much greater**. --- ## **Final Answer** ### - **Step 1:** - Molecules must be negatively charged. - Separation slows as gel permittivity increases. - High voltage risks overheating and separation errors. - Short electrodes cause field non-uniformity, impacting separation. ### - **Step 2:** - The electric field at the center of the gel, generated solely by the anode, is **much greater** than at the center of the (unpowered) cathode. - **Ratio:** The field at the center of the gel is essentially all that matters; at the cathode, the field is nearly zero. --- **If you want the exact electric field value, substitute the numbers into the formula above.** If you need the full numeric calculation, let me know!