Electric field equation

3 questions about Electric field equation

1. A conducting ball with a radius of 10 cm has an electric charge of 500 μC. Points A, B, and C lie in line with the center of the ball at a distance of 12 cm, 10 cm and 8 cm respectively from the center of the ball. Calculate the electric field strength at points A, B, and C!

Known:

The radius of the conducting ball (R) = 10 cm = 0.1 m

Electric charge (q) = 500 μC = 500 x 10^-6 C

r_A = 12 cm = 0,12 m

r_B = 10 cm = 0,1 m

r_C = 8 cm = 0,08 m

Coulomb constant (k) = 9 x 10⁹

Wanted: The electric field strength at point A (E_A), at point B (E_B) and at point C (E_C)

Solution:

a) The electric field strength at point A

E_A = k q / r_A² = (9 x 10⁹)(500 x 10^-6) / (0,12)² = (4500 x 10³) / 0,0144 = 312500 x 10³ = 3,125 x 10⁸ N/C

b) The electric field strength at point B

E_B = k q / r_B² = (9 x 10⁹)(500 x 10^-6) / (0,1)² = (4500 x 10³) / 0,01 = 450.000 x 10³ = 4,5 x 10⁸ N/C

c) The electric field strength at point C

E_C = 0 for being in the ball.

2. If a test charge of 4 nC is placed at a point, the charge experiences a force of 5 × 10 – 4 N. What is the magnitude of the electric field E at that point?

Known:

Test electric charge (q) = 4 nC = 4 x 10^-9 Coulomb

Electric force (F) = 5 × 10^-4 N

Wanted: The magnitude of the electric field (E)

Solution:

E = F / q = (5 × 10^-4) / (4 x 10^-9) = 1,25 x 10⁵ N/C

3. Two charges q_B = 12 μC and q_C = 9 μC are placed at the vertices of a right triangle as in Fig. Determine the electric field strength felt at point A!

Known:

Charge at point B (qB) = 12 μC = 12 x 10^-6 C

Charge at point C (qC) = 9 μC = 9 x 10^-6 C

Coulomb constant (k) = 9 x 10⁹

r_AC = 4 cm = 0,04 m

r_AB = 3 cm = 0,03 m

Wanted: electric field strength at point A

Solution:

E_AC = k q / r² = (9 x 10⁹)(9 x 10^-6) / (0,04)² = 81 x 10³ / 0,0016 = 5,0 x 10⁷ N/C

E_AB = k q / r² = (9 x 10⁹)(9 x 10^-6) / (0,03)² = 81 x 10³ / 0,0009 = 9,0 x 10⁷ N/C

Conceptual questions and answer about Electric field

1. Question: What is an electric field? Answer: An electric field is a region around a charged particle or object within which a force would be exerted on other charged particles or objects.
2. Question: What is the direction of the electric field produced by a positive charge? Answer: The electric field produced by a positive charge points outward, away from the charge.
3. Question: What is the direction of the electric field produced by a negative charge? Answer: The electric field produced by a negative charge points inward, towards the charge.
4. Question: What happens to the strength of the electric field as you move further away from the charge? Answer: The strength of the electric field decreases as you move further away from the charge. The field strength decreases inversely with the square of the distance from the source charge.
5. Question: How is the electric field related to the force experienced by a charge? Answer: The electric field (E) is related to the force (F) experienced by a charge (q) through the relationship E = F / q.
6. Question: What is Coulomb’s Law and how does it relate to the electric field? Answer: Coulomb’s Law describes the force between two charges. It states that the force (F) between two charges (q₁ and q₂) separated by a distance r is given by F = k x (q₁q₂) / r², where k is Coulomb’s constant. This force, when divided by a charge, gives the electric field.
7. Question: Can an electric field exist in a vacuum? Answer: Yes, an electric field can exist in a vacuum. It does not require a medium to propagate.
8. Question: What is the unit of electric field strength? Answer: The unit of electric field strength in the International System of Units (SI) is Newtons per Coulomb (N/C).
9. Question: Can electric field lines cross each other? Answer: No, electric field lines cannot cross each other. Each line indicates the direction of the field at a particular point, so if they crossed, the field would have two directions at that point, which is not possible.
10. Question: What does it mean if the electric field lines are close together? Answer: If the electric field lines are close together, it indicates a region of strong electric field.
11. Question: What does it mean if the electric field lines are far apart? Answer: If the electric field lines are far apart, it indicates a region of weak electric field.
12. Question: How does a uniform electric field look like? Answer: A uniform electric field is represented by equally spaced parallel lines. The direction of the lines indicates the direction of the field.
13. Question: How does the electric field behave near a sharp point of a conductor? Answer: The electric field is strongest near the sharp points or edges of a conductor. The field lines are more concentrated in these areas.
14. Question: Can a neutral object experience a force in an electric field? Answer: No, a neutral object does not experience a force in an electric field because the forces on the positive and negative charges of the neutral object cancel each other out.
15. Question: What is the effect of a medium on the electric field between two charges? Answer: The presence of a medium (other than vacuum) between two charges can reduce the electric field between the charges. The factor by which the field is reduced is called the relative permittivity or dielectric constant of the medium.
16. Question: How does an electric field affect an electric dipole? Answer: An electric field exerts a torque on an electric dipole, causing it to rotate. The net force on a dipole in a uniform electric field is zero, but the forces on the individual charges create a torque.
17. Question: What does the electric field inside a conductor look like in static equilibrium? Answer: In static equilibrium, the electric field inside a conductor is zero.
18. Question: How does a charge affect the electric field around it? Answer: A charge creates an electric field around it. The strength and direction of the field depend on the magnitude and sign of the charge.
19. Question: What is the significance of the electric field lines’ starting and ending points? Answer: Electric field lines originate on positive charges and end on negative charges. This indicates the direction that a positive test charge would move in the field.
20. Question: How does the superposition principle apply to electric fields? Answer: The superposition principle states that the net electric field produced by a collection of charges is the vector sum of the fields produced by each individual charge.