Coulomb's Law (Electric Force) Practice Problems

The sun emits ions and electrons that travel through space. Consider 0.00100 kg of electrons that have just escaped from the sun and an equal amount of electrons that have arrived at Mars's surface (in practice reaching a planet's surface may be thwarted by the atmosphere and a planet's magnetic field). i) What is the net electric force that the two groups of electrons exert on each other? Take the two sets of electrons to be stationary and behave like a point charge. ii) Should gravitational force from the sun and Mars be included in computing net force on the electron groups? iii) Calculate the gravitational force the two sets of electrons exert on each other. Assume their position is equal to the radius of the sun and Mars respectively. Hint: Find electrons' separation from the orbital radius of Mars. 

In an electrostatics virtual lab, small charged balls (can be approximated to point charges) are arranged as follows along the y-axis. Ball b₁ is placed at the origin. and ball b₂ at 3.00 cm. The charges of the balls are b₁ = 2.00 μC, b₂ = -4.00 μC, and b₃ = - 6.00 μC. The net force on b₁ is -5.00 N.  What position of b₃ results in that net force?

An electrostatics lab activity uses three charged spheres (that can be modeled as point charges) to study electric forces. Spheres s₃ is placed at the origin, s₂ at x = 4.00 cm, while s₁ is placed at 8.00 cm. Spheres s₃ and s₁ have charges -4.00 nC and 6.00 nC, respectively. What is the magnitude and sign of the charge s₂ if the net force from the other charges on s₁ is zero? 

Two glass balls are rubbed with silk to charge them positively. One ball has 5 times the charge on the other ball. When the balls are separated by 20.0 cm, the balls repel each other with a force of magnitude 0.280 N. Determine the charge on each sphere. 

Two glass balls acquire an equal positive charge when charged by rubbing them with silk. When the balls are separated by 22.0 cm, the magnitude of the repulsive force between them is 0.320 N. Determine the charge on each sphere. 

Two equally charged miniature steel ball bearings are positioned on insulating holders. The holders' separation is 16.0 cm. The balls repel each other with 5.0 × 10^-19 N. Determine the number of extra electrons on each ball.

Two charged copper balls are 55.0 cm apart. The mass of each ball is 0.0200 kg. Electrons are transferred from one ball to the other until the spheres experience an attractive force of 7500 N. Express the transferred electrons as a fraction of the total electrons in one ball. Treat the charged balls like point charges.

Two decorative copper balls are 45.0 cm apart. Each ball has a mass of 0.0240 kg. Determine the number of electrons that should be transferred from one ball to the other to create an attractive force between the balls of magnitude 8000 N. Treat the charged balls like point charges.

Three charges are positioned as shown in the figure. The charge q ₂ is proportional to q₁. Determine the coefficient of proportionality between q₁ and q₂, given that the net force acting on q₁ forms a 45° clockwise angle with the negative axis.

Two small objects, each with a mass of 4.0 g and unknown charges, are placed on a frictionless horizontal table at various distances apart. The magnitude of the charges on the objects is the same, but their signs are opposite. The resulting acceleration of one of the two objects is measured and recorded. The collected data is as follows:

By analyzing the relationship between distance and acceleration using an appropriate graph, determine the magnitude of the charges on the objects.

There are two small glass orbs with a mass of 3.0 g each and a charge of -40.0 nC. Both orbs are measured at 3.0 cm apart, relative to their centers. How much electric force do the orbs exert on each other?

A 1.5 g charged silicone block with a charge of -2.5 nC and a 0.5 g charged acrylic block with a charge of +4.2 nC are initially set 3.0 cm apart and permitted to move unimpeded. Compute the acceleration experienced by the silicone block.

A massless elastic band is fixed at one end, and a 20 nC charged object is fastened to the other end. A -40 nC charged object is carefully moved closer. When the charged objects are 1.8 cm apart, the elastic band stretches by 0.9 cm from its original length. Calculate the spring constant for the stretched elastic band.

Two friends, Emily and Fiona, are conducting a science experiment with static electricity. Each has a negatively charged plastic rod, Rod E and Rod F, with identical 30 g masses. However, Rod E carries six times the charge of Rod F. When they hold the rods 20 cm apart, Rod F experiences an electric force of 0.35 N due to the repulsion between them. What is the charge on Rod E?

Determine the force (F) acting on the 2.0 nC charge located at the bottom, as shown in the figure below. Provide your response by providing individual components.

We have three particles. One has a +3 nC charge located at the origin (point A), and another has a -5 nC charge (at point B), 3 cm away from the origin on the +x-axis. Find the distance from the origin to a point between the two particles at which a particle with a -1 nC charge experiences zero net force.

Two small plastic beads with equal charges are attached to a 10.0 cm long unstretched rubber band, causing it to stretch to a length of 13.0 cm due to electrostatic repulsion. The rubber band is stretched to 15.0 cm in a separate experiment by applying a force equivalent to a 0.1 g mass hanging vertically. Determine the magnitude of the charge (in nC) on each bead.

At a carnival, an 8.0 g charged metallic bee with a 4.0 nC charge is fastened to a 35 cm string. It orbits horizontally around a fixed metallic flower with a -6.0 nC charge at 275 rpm. Calculate the string's tension.

A 2.5×10²⁵ kg rogue planet with a charge of 6800 C is found. A 5.5×10⁴ kg spaceship with a charge of -2.3 C is to orbit it. What speed is needed for a 15000-km-diameter orbit?

A tiny plastic sphere charged with a net positive charge of +4.0 nC. It's located in the mid-plane of a uniformly charged, 8.0 cm-long plastic rod and is 3.0 cm away from its center. A force of 650 μN repels the sphere from the rod. Determine the rod's accumulated charge.

In a nanoscale electrostatic system, a tiny charged particle (similar to an electron) orbits a central charged core (similar to a proton) in a circular orbit with a radius of 0.053 nm. The central core's mass is significantly greater, allowing it to be considered at rest. What is the orbital frequency of the charged particle in revolutions per second?

We have three small balloons with static electric charges in a square arrangement. The first, second, and third balloons have charges of -8.0 nC, 6.0 nC, and 8.0 nC respectively. Compute the magnitude and angle (clockwise or counterclockwise from the +x-axis) of the net force acting on the 6.0 nC charged balloon.

A distance of 3.0 fm separates two neutrinos. How much gravitational force is exerted on one neutrino due to the other neutrino?  (The mass of a neutrino is 1.25 × 10^-37 kg).

Determine the net force acting on charge M as shown below. 

Determine the net force on 3.0-mC charge as shown in the figure below. 

On a smooth horizontal surface, a 3.1 kg coin is positioned 4.5 m from an identical coin with an equal charge. When the force holding them is removed, they accelerate at 55 m/s². Compute the magnitude of the charge on each coin.

A nano-scale tuning fork has two prongs with an initial distance of 4.20 cm between them. A small crystal sphere is attached to each prong. When a charge of -35 nC is applied to each sphere, the distance between the prongs increases by 0.68 cm. Calculate the spring constant of the tuning fork.

As shown in the diagram, two-point charges, Q₁ = -8.5 μC and Q₂ = 3.4 μC, are positioned between two oppositely charged parallel plates. The separation between the two charges is y = 0.35 m. The electric field generated by the charged plates is uniform and has a magnitude of E = 60000 N/C. Determine the magnitude of the net electrostatic force acting on Q₁ and specify its direction.

Imagine three identical charges, each with a magnitude of +20.0 μC. These charges are positioned at the corners of a triangle. The length of each side of the triangle is 10.0 cm. Determine the magnitude of the net force experienced by each charge. Also, the direction of the force caused by the mutual influence of the other two charges should be identified.

Two small charged spheres of charge q₁ = 30 μC and  q₂ = 45 μC are 10 cm apart as shown in the image.  Determine the net electric force exerted by the two spheres on a proton placed on the x-axis at i) x = 5 cm and ii) x = 15 cm.

Two electrons have a separation of 1.20 nm. They are both released simultaneously such that they are free to move. Determine the greatest acceleration and specify when it is observed. 

A linear particle accelerator accelerates two hydrogen ions to equal speeds toward each other. If the speed at infinite separation is 6.2 × 10⁵ m/s, determine the greatest electric force the two ions will exert on each other.

During an experiment, a  group of students placed a  negatively charged particle -q at x,y = 0,-2. A second negatively charged -Q particle is placed at x,y = -2,0. Make a sketch showing the locations of the charges. 

In a chemistry lab experiment, a student is studying the interactions between particles in an atom. She measures the distance between the nitrogen nucleus (q = +7e) and its innermost electron to be 1.8 x 10⁻¹² m. Calculate the magnitude of the electric force between them.

An electron orbits around a proton in an atom at a distance of approximately 0.75 × 10^-12 m away from it. Compare their electrical forces with their gravitational forces, what would be their ratio?

Two point charges -2q and -3q are separated by some fixed distance d. A third point charge (fixed) is so arranged that the system remains in equilibrium. What will this third point charge be and where will you arrange this third point?

Determine the points along the x-axis where the net electric field is zero. Imagine a positive point charge Q₁= 3.5 × 10^-5 C is placed at the origin and a negative point charge Q₂ = -6.0 × 10^-6 C is positioned at x = + 3.5 m. These charges create an electric field along the x-axis.

Imagine if Jupiter's moon Io was held in its orbit due to electrostatic forces instead of gravity with equal and opposite charges placed on Jupiter and Io respectively. What would be this charge (Q) required for Io to maintain its present orbit? Given that Jupiter's mass = 1.898 × 10²⁷ kg, Io's mass = 8932 × 10¹⁶ kg, and distance between them = 421700 km.

Four identical positive point charges each having value '+7μC' are located at the vertices of a square having a side length of 15 cm. What should be the magnitude and sign (positive/negative) of an additional point charge placed at the center so that all charges remain in equilibrium? Is this configuration stable or unstable?

On Mars, the surface has an upward electric field strength of about 100 N/C. The gravitational field strength there is about 3.71 N/Kg. A charged sphere weighing in at exactly 1.0 kg falls at an acceleration rate of exactly 1.85 m/s². What would be both magnitude and sign for this object’s charge?

An alpha particle (helium nucleus with a mass of about 6.64 x 10^-27 kg) moves in a circular path around an anti-proton with a radius of 0.350 × 10^-12 m. Calculate its speed and check if it's relativistic. [Hint: A particle is considered relativistic if its speed is above 0.100c.]

Two small conducting spheres M and N carrying equal charges E are kept at a distance L apart from each other. (i) What would be the electrostatic force exerted by N on M? (ii) Another uncharged identical conducting ball O comes in contact with N and is then moved very far. What would be the new net electrostatic force acting on M? (iii) Later, O comes back, touches M, and then moves very far. What would the new net electrostatic forces be acting on M?

A one-dimensional column of negative ions, each with a charge of "-q" and separated by distance "f" along the z-axis which starts from z = 0 towards positive infinity, which will mean that there are charges at z = 0, z = f, z = 2f, ... going on for infinity.

i. If we place an electron at position z = -f, what would be the magnitude of the electric force "F" experienced by this electron? Calculate the value of "F".

ii. If we were to place this electron at z = -3f instead, what would be the new value for "F"?

[Hint: $\sum_{n=1}^{\infty} \frac{1}{n^{2}}=\frac{\pi^{2}}{6}$]

Two positive point particles are kept at a fixed separation from each other with their combined electric charge represented by P. What must each particle carry in order to (i) increase the electric interaction between them maximally, (ii) decrease it minimally?