Umair Gaines
The repulsive electrical force between two protons in a nucleus that are very close together, approximately 5.0 x 10^-15 m apart, can be calculated using Coulomb's Law, which describes the electric force between two charges. This force is repulsive when the charges have the same sign and attractive when they have opposite signs. The formula for the force magnitude is kq1q2/r^2, where k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between them. By plugging in the given values and performing the necessary calculations, we can determine the repulsive electrical force acting between the two protons. This concept is crucial in understanding the behavior of charged particles and the fundamental forces governing their interactions.
| Characteristics | Values |
|---|---|
| Repulsive electrical force between two protons in a nucleus that are 5.0 x10-15 m apart | 9.2 N |
| Repulsive electrical force between two protons in a nucleus that are 4.0 x10-15 m apart | Not given, but the formula to calculate it is F = (9 x 109 Nm2/C2)(1.6 x 10-19 C)2 / (distance apart in meters)^2 |
| The electric force is attractive or repulsive | If the charges have opposite signs, it is attractive. If the charges have the same sign, it is repulsive. |
| Magnitude of the electric force | kq1q2/r2 |
| Magnitude of the gravitational force | Gm1m2/r2 |
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What You'll Learn
The force between two protons in a nucleus
The nuclear force, or residual strong force, acts between nucleons (protons and neutrons) to bind them together to form a nucleus. This force is carried by mesons and is a residual force of the strong force that acts between quarks. The strong force binds quarks together to form protons and neutrons. The strong force is much stronger than the nuclear force, and is one of the four fundamental forces, alongside the electromagnetic force, the weak force, and gravitation.
The nuclear force is essential in storing energy that is used in nuclear power and nuclear weapons. Work is required to bring charged protons together against their electric repulsion. This energy is stored when the protons and neutrons are bound together by the nuclear force to form a nucleus. The mass of a nucleus is less than the sum of the individual masses of the protons and neutrons, and this difference is known as the mass defect, which can be expressed as an energy equivalent.
At small separations between nucleons (less than 0.7 fm between their centres), the force becomes repulsive, which keeps the nucleons at a certain average separation. This repulsion arises from the Pauli exclusion force, which states that the spin vectors of two particles of the same type must point in opposite directions when the particles are near each other and are in the same quantum state. However, at distances larger than 0.7 fm, the force becomes attractive between spin-aligned nucleons, and becomes maximal at a centre-centre distance of about 0.9 fm. Beyond this distance, the force drops exponentially, until beyond about 2.0 fm separation, the force is negligible.
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The force between three charged particles
Coulomb's law can be used to calculate the force between two electrically charged particles at rest. It states that the magnitude of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them.
The electrostatic force between two charges is repulsive if the charges have the same sign and attractive if they have different signs. Coulomb's law can be used to determine the force between three charged particles. The net force on each particle due to the other two can be calculated by considering the x and y components of the forces acting on each particle.
For example, consider three charged particles, Q1, Q2, and Q3, placed in a line with Q2 and Q3 equidistant from Q1. The net force on Q1 due to Q2 and Q3 can be calculated by finding the x-component of the forces acting on Q1 due to Q2 and Q3. The x-component of the force between two charges is given by Coulomb's law, with the distance between the charges being the distance between the particles. The net force on Q1 in the x-direction is the vector sum of the x-components of the forces acting on it due to Q2 and Q3.
Similarly, the net force on Q2 due to Q1 and Q3 can be calculated by considering the x-components of the forces acting on Q2 due to Q1 and Q3. The net force on Q3 due to Q1 and Q2 can be calculated in the same way. The net force on each particle due to the other two can then be found by considering both the magnitude and direction of the x-components of the forces.
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The electric force holding an electron in orbit
The electric force is responsible for holding an electron in orbit around a proton. This is also known as Coulomb's law, which is very similar in form to Newton's law of universal gravitation. However, the gravitational force is always attractive, whereas the electric force is attractive only if the charges have opposite signs and repulsive if the charges have the same sign.
In a hydrogen atom, the electric force is the centripetal force that holds the electron in orbit around the proton. The mass of an electron is 9.11 x 10^-31 kg, and the distance between the electron and proton is about 5.3 x 10^-11 m. The electric force between them is approximately 1.48 x 10^45 times stronger than the gravitational force. This significant difference highlights the dominance of electromagnetic interactions compared to gravitational interactions at the atomic scale.
The electron is attracted to the nucleus of an atom but remains in an orbital around it. Niels Bohr originally modelled the electron similarly to planets orbiting the Sun, but it is now known that the electron has probable locations where it may reside in an orbital. The proton consists of both negative and positive particles that attract and repel the electron. As spherical longitudinal waves converge on these particles, each particle rapidly spins, creating a transverse wave.
The transverse wave of the proton causes a repelling force, known as the orbital force, which keeps the electron in orbit. Meanwhile, the electron is also attracted to the positron in the proton with destructive, longitudinal wave interference (electric force). The resulting sum of these waves and their amplitudes creates a position where the forces are equal, and the electron establishes its orbit.
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The electric force compared to gravitational force
The gravitational force between two objects is governed by Newton's law of universal gravitation, which dictates a direct proportionality between the force and the product of the masses of the objects, and an inverse proportionality with the square of the distance between them. The gravitational force constant (G) is relatively small, making the gravitational force weak in comparison to the electric force.
The electric force, on the other hand, is described by Coulomb's law, which is very similar in form to Newton's law. The key difference is that while the gravitational force is always attractive, the electric force can be either attractive or repulsive, depending on the charges of the objects. If the charges have the same sign, the electric force is repulsive, and if they have opposite signs, it is attractive.
The magnitude of the gravitational force between two 100-gram apples placed 1 metre apart is extremely small, approaching zero. In contrast, if one apple is charged with +1 coulomb and the other with -1 coulomb, the electric force between them becomes unimaginably large. This thought experiment illustrates the significant disparity between the strengths of the electric and gravitational forces.
In everyday life, we rarely experience the electric force because almost every negative charge (electron) is closely accompanied by a positive charge (the nucleus of an atom), resulting in neutralization. On a larger scale, however, such as in the interactions between celestial bodies, the cumulative effect of their large masses causes the gravitational force to dominate over the electric force.
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The force between two smoke particles
In the context of electrical forces, the concept of repulsion comes into play when charges have the same sign. Coulomb's law, which is similar in form to Newton's law of universal gravitation, describes the relationship between electric charges and the resulting forces. While gravitational forces are always attractive, electric forces can be either attractive or repulsive, depending on the charges involved.
When two charged smoke particles interact, the force between them depends on the nature of their charges. If the charges have opposite signs, the force between them is attractive. However, if the charges have the same sign, the force becomes repulsive. This repulsive electrical force between two similarly charged smoke particles is a direct result of the like charges exerting a pushing force on each other.
For example, let's consider two charged smoke particles with a distance of one-eighth between them. If these particles exert an initial force of 4.2 x 10-2 N on each other, the force between them at the reduced distance can be calculated using Coulomb's law. By adjusting the distance in the formula kq1q2/r^2, we can determine the new force magnitude.
In summary, the force between two smoke particles, particularly in the context of electrical forces, depends on the charges they carry. When the charges are of the same sign, the force between the smoke particles becomes repulsive, causing the particles to exert a pushing force on each other.
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Frequently asked questions
The force is calculated to be 9.2 N.
The force is calculated to be 9.2 x 10^3 N.
The gravitational force is always attractive, whereas the electric force can be attractive or repulsive depending on the charges involved.
