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 = 9.10^{9} N.m^{2}.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) = 9.10^{9} N.m^{2}.C^{-2}

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

__Solution :__

V = k Q / r

V = (9 x 10^{9})(4 x 10^{-6}) / (8 x 10^{-2})

V = (36 x 10^{3}) / (8 x 10^{-2})

V = (36/8) x 10^{3} x 10^{2}

V = 4.5 x 10^{5 }Volt

2. A spherical conductor has radius of 3-cm (1 μC = 10^{-6 }C and k = 9.10^{9} N.m^{2}.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) = 9.10^{9} N.m^{2}.C^{-2}

__Wanted :__ The electric potential at point A (V)

__Solution :__

V = k Q / r

V = (9 x 10^{9})(1 x 10^{-6}) / (3 x 10^{-2})

V = (9 x 10^{3}) / (3 x 10^{-2})

V = (9/3) x 10^{3} x 10^{2}

V = 3 x 10^{5 }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 = 9.10^{9} N.m^{2}.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) = 9.10^{9} N.m^{2}.C^{-2}

__Wanted :__ The electric potential at point P (V)

__Solution :__

V = k Q / r

V = (9 x 10^{9})(6,4 x 10^{-9}) / (9 x 10^{-2})

V = 10^{9 }(6,4 x 10^{-9}) / 10^{-2}

V = 6.4 / 10^{-2}

V = 6.4 x 10^{2}

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?

**Answer:** 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. Question:** How does the presence of a dielectric material near a charged conducting ball affect its electric potential?

**Answer:** A dielectric material affects the electric field near the conductor, which can influence the potential. Typically, dielectrics reduce the effective electric field.

**20. Question:** What is the electric potential at a point infinitely far from a charged conducting ball?

**Answer:** 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.