 # Electric potential at the conductor of ball – problems and solutions

Electric potential at the conductor of ball – problems and solutions

1. A 4-μC hollow ball conductor has radius of 8-cm. Determine the electric potential at the surface of the ball. (k = 9.109 N.m2.C-2)

Known :

The electric charge (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 N.m2.C-2

Wanted : The electric potential at the surface of the ball (V)

Solution :

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

V = 4.5 x 105 Volt

2. A spherical conductor has radius of 3-cm (1 μC = 10-6 C and k = 9.109 N.m2.C-2). If the conductor is positively charged +1 μC then the electric potential at point A is …

Solution :

The electric potential inside the spherical conductor = The electric potential at the surface of the spherical conductor.

Known :

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 N.m2.C-2

Wanted : The electric potential at point A (V)

Solution :

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

V = 3 x 105 Volt

3. A hollow metal ball with radius of 9-cm has 6.4 x 10-9 Coulomb electric charge, as shown in figure below. Distance 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 N.m2.C-2. Determine the electric potential at point P.

Solution

The electric potential inside the spherical conductor = The electric potential at the surface of the spherical conductor.

Known :

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 N.m2.C-2

Wanted : The electric potential at point P (V)

Solution :

V = k Q / r

V = (9 x 109)(6,4 x 10-9) / (9 x 10-2)

V = 109 (6,4 x 10-9) / 10-2

V = 6.4 / 10-2

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V = 6.4 x 102

V = 6.4 x 100

V = 640 Volt

1. Question: What is electric potential?

Answer: Electric potential is the electric potential energy per unit charge at a specific point in space.

2. Question: How is the electric potential on the surface of a conducting ball defined?

Answer: 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. Question: Why is the electric potential constant everywhere on the surface of a charged conducting ball?

Answer: 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. Question: How does the potential vary inside a conducting ball?

Answer: 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. Question: How does the size of the conducting ball affect its surface potential, given a constant charge?

Answer: A larger ball (greater R) would have a smaller surface potential for a given charge Q, based on the formula V = kQ/R.

6. Question: How is electric potential related to electric field?

Answer: 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. Question: Why can’t we have an electric field inside a conducting ball in electrostatic equilibrium?

Answer: 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. Question: What would happen to the electric potential of a conducting ball if the amount of charge on it were doubled?

Answer: Doubling the charge Q would double the electric potential V, given the relation V = kQ/R.

9. Question: What is the significance of the term ‘k’ in the formula for electric potential?

Answer: ‘k’ is Coulomb’s constant, which is approximately 8.99 x 10⁹ N.m²/C² in vacuum.

10. Question: How is electric potential energy different from electric potential?

Answer: 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. Question: Does a charged conducting ball influence the electric potential of nearby objects?

Answer: Yes, any charged object creates an electric field in its surroundings, which affects the electric potential of nearby objects.

12. Question: How is the electric potential at a point near a charged conducting ball calculated?

Answer: It’s calculated using the formula V = kQ/r, where r is the distance from the center of the ball to the point.

13. Question: If two identical conducting balls, one charged and one uncharged, are brought into contact and then separated, what happens to the potential of each?

Answer: The charge will distribute equally between the two balls, making their potentials identical.

14. Question: What is the role of the grounding process in affecting the potential of a conducting ball?

Answer: Grounding a conductor allows it to exchange charge with the Earth until its potential becomes zero.

15. Question: Why is the electric potential zero inside a grounded conducting ball?

Answer: When grounded, a conductor exchanges charges with the Earth until the electric field inside it is nullified, making the potential zero.

16. Question: Does the shape of a conductor affect its surface potential?

Answer: 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. Question: How does the distribution of charge vary on a non-spherical conductor?

Answer: On a non-spherical conductor, charge tends to accumulate more at sharp points or edges due to the concentration of electric field lines.

18. Question: Why can birds sit on high voltage power lines without getting electrocuted?