Listrik Statis • Part 4: Contoh Soal Gaya Listrik dan Energi Potensial Listrik

Main Ideas & Concepts Covered

• Static electricity / electric forces at high school Grade 12 level, continuing from previous parts.
• Electric potential and motion of charged particles:
  • Use conservation of energy to connect voltage (potential difference) to kinetic energy, and therefore determine speed.
• Electrostatics with multiple like charges:
  • Two identical like charges hanging on a light rope repel each other.
  • The repulsive electric force is balanced by tension and weight via force equilibrium:
    • (\sum F_x = 0) and (\sum F_y = 0)

Core Formulas / Methods Used

• Energy conservation: [ q\Delta V=\Delta\left(\tfrac12 mv^2\right) ]

• Coulomb’s law (electrostatic force): [ F = k \frac{|Q_1Q_2|}{r^2} ]

• Equilibrium approach:

  • Resolve forces into components and set the sums to zero.

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Detailed Worked Methodology From the Subtitles

1) Electron accelerated by a potential difference (speed at the anode)

Given

• Electron mass: (m = 9 \times 10^{-31}\,\text{kg})
• Electron charge magnitude: (|q| = 1.6 \times 10^{-19}\,\text{C})
• Electron moves from cathode to anode
• Potential difference: (\Delta V = 4500\,\text{V})
• Starts from rest at cathode: (v_1 = 0)
• Find speed at anode: (v_2)

Steps

1. Relate the voltage change: [ V_1 - V_2 = \Delta V = 4500 ] (Treated as the potential difference between cathode and anode.)

2. Apply energy conservation between cathode and anode: [ q(V_1 - V_2)=\tfrac12 mv_2^2-\tfrac12 mv_1^2 ]

3. Since (v_1=0): [ q(V_1 - V_2)=\tfrac12 mv_2^2 ]

4. Solve for (v_2): [ v_2=\sqrt{\frac{2q(V_1 - V_2)}{m}} ]

5. Substituting values (as stated in the subtitles) gives:

   • Speed at the anode: [ v_2 = 4 \times 10^{7}\ \text{m/s} ]

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2) Two identical like charges on a rope forming a 60° angle

Given (geometry & physical setup)

• Two identical charges hang on a rope (rope mass ignored).
• Rope forms an angle of (60^\circ) (symmetric forces).

• Each charge has the same mass: [ m = 400\sqrt{3}\ \text{mg} ]

• Rope length: 9 cm (referenced in the subtitles)

• The charges repel, setting the separation that produces the angle.

Unknowns

• (a) Magnitude of each charge (Q)
• (b) Rope tension (T)

Steps to Solve (force equilibrium)

1. Use symmetry / analyze one side

   • Forces on one charge include:
     • Weight (W) downward
     • Tension (T) along the rope (tilted)
     • Electric repulsion (F) horizontally (pushing away)

2. Resolve tension into components (with (60^\circ))

   • Horizontal: (T\cos 60^\circ)
   • Vertical: (T\sin 60^\circ)

3. Write equilibrium equations

   • Horizontal equilibrium: [ \sum F_x = 0:\quad T\cos 60^\circ - F = 0 ] The subtitles conclude: [ T = 2F ]

   • Vertical equilibrium: [ \sum F_y = 0:\quad T\sin 60^\circ - W = 0 ] Substitute (T=2F) and use the given weight.

4. Compute weight

   • Convert mass to kilograms (as done in the subtitles), then: [ W = mg ]

   • The subtitles’ stated intermediate result leads to: [ F = 4\times 10^{-3}\ \text{N} ]

5. Use Coulomb’s law to find charge

   • For identical charges: [ F = k\frac{Q^2}{r^2} ]

   • The separation distance is taken from geometry (rope length and the (60^\circ) angle), stated in the subtitles as: [ r = 9\times 10^{-2}\ \text{m} ]

   • Solve for (Q): [ Q = \sqrt{\frac{Fr^2}{k}} ]

   • Subtitles give the final result: [ Q = 6 \times 10^{-8}\ \text{C} ]

6. Compute rope tension

   • Using (T=2F): [ T = 8 \times 10^{-3}\ \text{N} ]

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Other Points Mentioned

• The video is presented as a continuation of example questions from “Part 3”; viewers are instructed to watch previous parts for full context.
• The subtitles reference a broader topic list (electric force, electric field, electric flux, electric potential, electric potential energy), though the detailed work shown focuses on the two examples above.
• Channel prompts like subscribe/notification are included but are not part of the physics content.

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Speakers / Sources Featured

• Christian Sutantio (host / instructor)
• Science Window channel (referenced source)