በኳሱ መሪ ላይ የኤሌክትሪክ አቅም - ችግሮች እና መፍትሄዎች
1. A 4-μC hollow ball conductor has radius of 8-cm. Determine the የኤሌክትሪክ አቅም at the surface of the ball. (k = 9.109 Nm2.C-2)
የሚታወቅ፦
የ የኤሌክትሪክ ክፍያ (Q) = 4 μC = 4 x 10-6 C 
The radius of ball (r) = 8 cm = 8 x 10-2 m
Coulomb’s constant (k) = 9.109 Nm2.C-2
የሚፈለግ፦ The electric potential at the surface of the ball (V)
መፍትሔው
V = k Q / r
V = (9 x 109)(4 x 10-6) / (8 x 10-2)
V = (36 x 103) / (8 x 10-2)
V = (36/8) x 103 x 102
ቪ = 4.5 x 105 ቮልት
2. A spherical conductor has radius of 3-ሴሜ (1 μC = 10-6 C and k = 9.109 Nm2.C-2). If the conductor is positively charged +1 μC then the electric potential at point A is …
መፍትሔው
The electric potential inside the spherical conductor = The electric potential at the surface of the spherical conductor.
የሚታወቅ፦
The electric charge (Q) = 1 μC = 1 x 10-6 C 
The radius of the spherical conductor (r) = 3 cm = 3 x 10-2 m
Coulomb’s constant (k) = 9.109 Nm2.C-2
የሚፈለግ፦ The electric potential at point A (V)
መፍትሔው
V = k Q / r
V = (9 x 109)(1 x 10-6) / (3 x 10-2)
V = (9 x 103) / (3 x 10-2)
V = (9/3) x 103 x 102
ቪ = 3 x 105 ቮልት
3. A hollow metal ball ጋር ራዲየስ of 9-ሴሜ has 6.4 x 10-9 Coulomb electric charge, as shown in figure below. ርቀት between point O and point P = 4 cm; Distance between point P and point Q = 5 cm; Distance between point Q and point R = 18 cm and k = 9.109 Nm2.C-2. Determine the electric potential at point P.
መፍትሔ
The electric potential inside the spherical conductor = The electric potential at the surface of the spherical conductor.
የሚታወቅ፦
The electric charge (Q) = 6.4 x 10-9 C
The radius of the spherical conductor (r) = OP + PQ = 4 cm + 5 cm = 9 cm = 9 x 10-2 m
Coulomb’s constant (k) = 9.109 Nm2.C-2
የሚፈለግ፦ The electric potential at point P (V)
መፍትሔው
V = k Q / r
V = (9 x 109)(6,4 x 10-9) / (9 x 10-2)
ቪ = 109 (6,4x10)-9) / 10-2
V = 6.4 / 10-2
ቪ = 6.4 x 102
ቪ = 6.4 x 100
ቪ = 640 ቮልት
1. ጥያቄ What is electric potential?
መልስ: Electric potential is the electric potential energy per unit charge at a specific point in space.
2. ጥያቄ How is the electric potential on the surface of a conducting ball defined?
መልስ: The electric potential on the surface of a conducting ball is uniform and is given by the formula V = kQ/R, where Q is the charge on the ball and R is its radius.
3. ጥያቄ Why is the electric potential constant everywhere on the surface of a charged conducting ball?
መልስ: Conductors in electrostatic equilibrium have an electric field that’s perpendicular to the surface. Hence, no work is done in moving a charge on the surface, keeping the potential constant.
4. ጥያቄ How does the potential vary inside a conducting ball?
መልስ: Inside a uniformly charged conducting ball, the electric potential varies, but in the case of a hollow conducting ball, the potential remains constant inside and equals the potential on its surface.
5. ጥያቄ How does the size of the conducting ball affect its surface potential, given a constant charge?
መልስ: A larger ball (greater R) would have a smaller surface potential for a given charge Q, based on the formula V = kQ/R.
6. ጥያቄ How is electric potential related to electric field?
መልስ: Electric potential and electric field are related by the equation E = -dV/dr, where dV is the change in potential and dr is the change in position.
7. ጥያቄ Why can’t we have an electric field inside a conducting ball in electrostatic equilibrium?
መልስ: Electrons in a conductor move until they cancel out any external electric fields. Once equilibrium is reached, the electric field inside the conductor becomes zero.
8. ጥያቄ What would happen to the electric potential of a conducting ball if the amount of charge on it were doubled?
መልስ: Doubling the charge Q would double the electric potential V, given the relation V = kQ/R.
9. ጥያቄ What is the significance of the term ‘k’ in the formula for electric potential?
መልስ: ‘k’ is Coulomb’s constant, which is approximately 8.99 x 10⁹ N.m²/C² in vacuum.
10. ጥያቄ How is electric potential energy different from electric potential?
መልስ: Electric potential energy is the energy a charge has due to its position in an electric field, while electric potential is the electric potential energy per unit charge.
11. ጥያቄ Does a charged conducting ball influence the electric potential of nearby objects?
መልስ: Yes, any charged object creates an electric field in its surroundings, which affects the electric potential of nearby objects.
12. ጥያቄ How is the electric potential at a point near a charged conducting ball calculated?
መልስ: It’s calculated using the formula V = kQ/r, where r is the distance from the center of the ball to the point.
13. ጥያቄ If two identical conducting balls, one charged and one uncharged, are brought into contact and then separated, what happens to the potential of each?
መልስ: The charge will distribute equally between the two balls, making their potentials identical.
14. ጥያቄ What is the role of the grounding process in affecting the potential of a conducting ball?
መልስ: Grounding a conductor allows it to exchange charge with the Earth until its potential becomes zero.
15. ጥያቄ Why is the electric potential zero inside a grounded conducting ball?
መልስ: When grounded, a conductor exchanges charges with the Earth until the electric field inside it is nullified, making the potential zero.
16. ጥያቄ Does the shape of a conductor affect its surface potential?
መልስ: For a given charge, the distribution may vary with shape, but in electrostatic equilibrium, the potential remains constant across the surface of any conductor.
17. ጥያቄ How does the distribution of charge vary on a non-spherical conductor?
መልስ: On a non-spherical conductor, charge tends to accumulate more at sharp points or edges due to the concentration of electric field lines.
18. ጥያቄ Why can birds sit on high voltage power lines without getting electrocuted?
መልስ: Birds don’t get electrocuted because they are not completing a circuit. The electric potential is constant all over their body as they touch only one wire, so there’s no potential difference.
19. ጥያቄ How does the presence of a dielectric material near a charged conducting ball affect its electric potential?
መልስ: A dielectric material affects the electric field near the conductor, which can influence the potential. Typically, dielectrics reduce the effective electric field.
20. ጥያቄ What is the electric potential at a point infinitely far from a charged conducting ball?
መልስ: The electric potential approaches zero as one moves infinitely far from the charged source.
Understanding the nuances of electric potential, especially with conductors like balls, provides insights into many phenomena in electrostatics and real-world applications.
