Exam 25: The Electric Potential

A -7.0-μC point charge has a positively charged object in an elliptical orbit around it.If the mass of the positively charged object is 1.0 kg and the distance varies from 5.0 mm to 20.0 mm between the charges,what is the maximum electric potential difference through which the positive object moves? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart.If it takes of work to bring them to a final configuration in which the object i is at x = 1.00 mm,y = 1.00 mm,and the other charged object is at x = 1.00 mm,y = 3.00 mm,find the magnitude of the charge on the second object.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A charge Q = -610 nC is uniformly distributed on a ring of 2.4-m radius.A point charge q = +480 nC is fixed at the center of the ring,as shown in the figure.An electron is projected from infinity toward the ring along the axis of the ring.This electron comes to a momentary halt at a point on the axis that is 5.0 m from the center of the ring.What is the initial speed of the electron at infinity? (e = 1.60 × 10^-19 C,k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², m_el = 9.11 × 10^-31 kg )

If an electron is accelerated from rest through a potential difference of 9.9 kV,what is its resulting speed? (e = 1.60 × 10^-19 C,k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², ^m_el = 9.11 × 10^-31 kg)

Suppose a region of space has a uniform electric field,directed towards the right,as shown in the figure.Which statement about the electric potential is true?

Two point charges of +1.0 μC and -2.0 μC are located 0.50 m apart.What is the minimum amount of work needed to move the charges apart to double the distance between them? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively.Where should a third charge of +3.0-μC be placed on the +x-axis so that the potential at the origin is equal to zero? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

If the electric field is zero everywhere inside a region of space,the potential must also be zero in that region.

Suppose you have two negative point charges.As you move them farther and farther apart,the potential energy of this system relative to infinity

An electron is released from rest at a distance of 9.00 cm from a proton.If the proton is held in place,how fast will the electron be moving when it is 3.00 cm from the proton? (m_el = 9.11 × 10^-31 kg,e = 1.60 × 10^-19 C,k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. The excess charge on this sphere is closest to

If the electric potential at a point in space is zero,then the electric field at that point must also be zero.

Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of 1500 V/m,in the positive x-direction,is produced by charges on the plates.The center plane at x = 0.00 m is an equipotential surface on which V = 0.An electron is projected from x = 0.00 m,with an initial velocity of 1.0 × 10⁷ m/s perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A? (e = 1.60 × 10^-19 C,m_el = 9.11 × 10^-31 kg)

A charge Q = -820 nC is uniformly distributed on a ring of 2.4 m radius.A point charge q = +530 nC is fixed at the center of the ring.Points A and B are located on the axis of the ring,as shown in the figure.What is the minimum work that an external force must do to transport an electron from B to A? (e = 1.60 × 10^-19 C,k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

The figure shows two arcs of a circle on which charges +Q and -Q have been spread uniformly.What is the value of the electric potential at the center of the circle?

A -3.0-μC point charge and a -9.0-μC point charge are initially extremely far apart.How much work does it take to bring the -3.0-μC charge to x = 3.0 mm,y = 0.00 mm and the -9.0-μC charge to x = -3.0 mm,y = 0.00 mm? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

If the electrical potential in a region is constant,the electric field must be zero everywhere in that region.

A negative charge is moved from point A to point B along an equipotential surface.Which of the following statements must be true for this case?

An alpha particle is a nucleus of helium.It has twice the charge and four times the mass of the proton.When they were very far away from each other,but headed toward directly each other,a proton and an alpha particle each had an initial speed of 0.0030c,where c is the speed of light.What is their distance of closest approach? Hint: There are two conserved quantities.Make use of both of them. (c = 3.00 × 10⁸ m/s,k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²,e = 1.60 × 10^-19 C, M_proton = 1.67 × 10^-27 kg)

Two positive point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) (a)What is the potential at point A (relative to infinity)due to these charges? (b)What is the potential at point B (relative to infinity)due to these charges?