Exam 15: Electric Charge force and Energy

A point charge of +3.00 μC and a second charge Q are initially very far apart.If it takes $29.0 \mathrm {~J}$ of work to bring them to a final configuration in which the $+ 3.00 - \mu \mathrm { C }$ charge is at the point x = 1.00 mm,y = 1.00 mm,and the second charge Q is at the point x = 1.00 mm,y = 3.00 mm,find the magnitude of the charge Q.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Consider a container of 2.0 g of hydrogen,H2 (one mole).Suppose you removed all the electrons and moved them to the other side of Earth (Earth's radius is 6380 km,k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²,N_A = 6.022 × 10²³ molecules/mol,e = 1.60 × 10^-19 C) (a)How much charge is left behind after you remove the electrons? (b)What electric force do the protons exert on the electrons after they are separated as described?

A very small 4.8-g particle carrying a charge of +9.9 μC is fired with an initial speed of $8.0 \mathrm {~m} / \mathrm { s }$ directly toward a second small 7.8-g particle carrying a charge of + $5.2 \mu \mathrm { C } \text {. }$ The second particle is held fixed throughout this process.If these particles are initially very far apart,what is the closest they get to each other? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Two tiny particles carrying like charges of the same magnitude are $1.0 \mathrm {~mm}$ apart.If the electric force exerted on one of them is $5.0 \mathrm {~N} \text {, }$ what is the magnitude of the charge on each of these particles?(k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Two protons are fired toward each other in a particle accelerator,with only the electrostatic force being exerted.Which of the following statements must be true about them as they move closer together? (There could be more than one correct choice.)

Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart.When released,they begin to accelerate away from each other at $414 \mathrm {~m} / \mathrm { s } ^ { 2 }$ What is the magnitude of the charge on each sphere,assuming only that the electric force is present? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Four point charges of equal magnitude but with varying signs are arranged on three of the corners and at the center of the square of side d as shown in the figure.Which one of the arrows shown represents the sum of the forces exerted on the center charge?

Two point charges q = -8.50 µC are fixed 10.0 cm apart along a horizontal bar,as shown in the figure.Their electrical forces will be used to balance the force that Earth exerts on a very small sphere carrying a charge $Q = + 15.0 \mu \mathrm { C }$ 10.0 cm from each of them in a place where g = 9.80 m/s².What is the greatest mass M this sphere can have without falling? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

As shown in the figure,the charge Q is midway between two other charges.If $Q = - 7.5 n C$ what must be the charge q1 so that charge q2 remains stationary as Q and q1 are held in place?

Two tiny particles having charges of +7.00 μC and -9.00 μC are placed along the y-axis.The +7.00-µC particle is at y = 0.00 cm,and the other particle is at y = 40.00 cm.Where must a third charged particle be placed along the y-axis so that the net electric force exerted on it by the other two particles is zero?

Two protons are released from rest,with only the electrostatic force exerted on them.Which of the following statements must be true about them as they move apart? (There could be more than one correct choice.)

Four charged particles (two having a charge +Q and two having a charge -Q)are arranged in the xy-plane as shown in the figure.The charges are all equidistant from the origin.The amount of work required to move a positively charged particle from point P to point O (both of which are on the z-axis)is

A particle of charge +2q is placed at the origin and particle of charge -q is placed on the x-axis at x = 2a.Where on the x-axis can a third positive charge be placed so that the net electric force exerted on it is zero?

Four point charges Q of equal magnitude and sign are arranged on three of the corners of the square of side d as shown in the figure.Which one of the arrows shown represents the sum of the forces exerted on the charge at the upper right hand corner of the square?

A small charged plastic ball is vertically above another charged small ball in a frictionless test tube as shown in the figure.The balls are in equilibrium a distance d apart.If the charge on each ball is doubled,the equilibrium distance between the balls in the test tube would become

If two objects are electrically attracted to each other,

Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure.If these charges are released and are free to move with no friction,what is the maximum amount of kinetic energy they will gain? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Three point charges are placed on the x-axis,as follows.A charge of +2.0 μC is at the origin,a charge of -2.0 μC is at x = 50 cm,and a charge of +4.0 μC is at x = 100 cm.What are the magnitude and direction of the net electrostatic force exerted on the charge at the origin by the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

One point charge +Q is placed at the center of a square,and a second point charge -Q is placed at the upper-left corner of the square.It is observed that an electrostatic force of magnitude 2.0 N is exerted on the positive charge at the center.Now a third charge -Q is placed at the lower-left corner of the square,as shown in the figure.What is the magnitude of the net force that is exerted on the center charge now?

As shown in the figure,three charges are at corners of a rectangle.The charge in the bottom right corner is Q = - 90 nC,and all the other quantities are accurate to two significant figures.What is the magnitude of the net electrical force exerted on Q by the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)