Electromagnetism: Charge and Coulomb's Law

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Questions and Answers

What is the significance of the quantization of charge at the macroscopic level?

It affects the flow of current in electrical circuits.

It results in inconsistencies in measurements.

It leads to practical applications in daily life.

It can be ignored as it has no practical consequence. (correct)

How long would it take to accumulate a total charge of 1 C if 10^9 electrons move out every second?

500 years

198 years (correct)

30 years

100 years

How many electrons are contained in one cubic centimeter of copper?

1.5 × 10^24

2.5 × 10^24 (correct)

4.5 × 10^24

3.5 × 10^24

In the context of a cup of water, how are the total positive and negative charges related?

They have the same magnitude. Signup and view all the answers

What is the mass of one mole of water, which contains a specific number of molecules?

18 g Signup and view all the answers

What can be concluded about the unit of charge, one coulomb, based on the examples provided?

It is a large unit for practical purposes. Signup and view all the answers

What calculation is used to determine the number of molecules in a cup of water?

Mass divided by molecular mass times Avogadro's number. Signup and view all the answers

Why can charge be said to take continuous values at a macroscopic level?

Because the quantization of charge is negligible. Signup and view all the answers

What is the expression for the force F1 on a charge Q due to charge q at point A?

$\frac{3Qq}{4\pi\epsilon_0 l^2}$ along AO Signup and view all the answers

How is the resultant force from F2 and F3 determined?

By the parallelogram law of vector addition Signup and view all the answers

What distance is AO from A if the perpendicular height AD of the triangle is given as (3/2)l?

(1/3)l Signup and view all the answers

Considering symmetry in the equilateral triangle, what can be said about the distances AO, BO, and CO?

AO = BO = CO Signup and view all the answers

Which principle underlies the calculations of forces on charge Q in an electrostatic arrangement?

Coulomb's law and superposition principle Signup and view all the answers

The forces F2 and F3 acted along which lines in relation to point O?

Along lines from vertices to the centroid Signup and view all the answers

If the charges q1, q2, and q3 are placed at the vertices of an equilateral triangle, what can be inferred about the forces acting on charge Q?

They exert a resultant force directed towards the centroid. Signup and view all the answers

What is the role of the perpendicular AD drawn to side BC in evaluating the force on charge Q?

To aid in calculating the centroid distance Signup and view all the answers

What is the role of the source charge Q in the context of an electric field?

It creates the electric field experienced by a test charge. Signup and view all the answers

How is the electric field E defined mathematically in relation to force F and test charge q?

E = F/q Signup and view all the answers

Why must the test charge q be negligibly small when defining the electric field?

To avoid disturbing the source charge Q. Signup and view all the answers

What does the statement 'the electric field E due to Q is independent of q' imply?

The force on the test charge is unaffected by its characteristics. Signup and view all the answers

Which statement correctly describes the behavior of the electric field at different positions in space?

The electric field exists at every point but varies with space coordinates. Signup and view all the answers

What does the term 'test charge' refer to?

The unit positive charge used for measuring electric field strength. Signup and view all the answers

Which factor is primarily responsible for holding the source charge Q in place during measurements?

The reactions from surrounding charges within the system. Signup and view all the answers

What is the implication of electrical forces acting on the source charge Q when a test charge q is introduced?

Q is acted upon by a force due to the presence of q. Signup and view all the answers

What is the formula for calculating the acceleration of an electron in an electric field?

ae = eE/me Signup and view all the answers

Given that the mass of a proton is 1.67 × 10–27 kg, what is the corresponding formula for its acceleration in an electric field?

ap = eE/mp Signup and view all the answers

What time does the electron take to fall a distance h in an electric field of strength E?

te = 2h/(meE) Signup and view all the answers

How does the time of fall for a proton compare to that of an electron when falling through the same distance?

The time of fall for the proton is greater than that of the electron. Signup and view all the answers

What is ignored in the calculation of the time of fall for both the electron and the proton?

Acceleration due to gravity Signup and view all the answers

If the electric field strength is doubled, how will the time of fall for both the electron and the proton be affected?

The time of fall will be halved. Signup and view all the answers

Which of the following statements contrasts with free fall under gravity?

Time of fall is independent of charge. Signup and view all the answers

What is the value of te calculated for an electron falling through a distance of 1.5 × 10–2 m in a field of strength E = 2.0 × 10^4 N/C?

2.9 × 10–9 s Signup and view all the answers

What is the formula for the electric field at a far-away point on the axis of a dipole?

$E = \frac{2p}{4 \pi \epsilon_0 r^3}$ Signup and view all the answers

In the given example, what is the resultant electric field at point P due to the two charges?

$2.7 \times 10^5 \text{ N C}^{-1}$ Signup and view all the answers

What represents the dipole moment in the electric field formula provided?

$p = 2a q$ Signup and view all the answers

How does the distance ratio OP/OB affect the electric field at point P in the example?

It becomes negligible when the distance is large. Signup and view all the answers

What does the term 60 refer to in the context of the ratio OP/OB?

The approximation factor for electric field calculations. Signup and view all the answers

What is the effect of increasing distance 'r' on the electric field 'E' according to the provided formula?

E decreases as $r^3$. Signup and view all the answers

Which constant is represented by $\epsilon_0$ in the electric field formula?

Vacuum permittivity Signup and view all the answers

When calculating the electric field due to point charges, which value is crucial for determining the force experienced by a charge at point P?

Both the charge magnitudes and their distances Signup and view all the answers

Study Notes

Quantization of Charge

Charge can only increase or decrease in units of e (the charge of an electron)
At a macroscopic level, the quantization of charge is negligible due to large numbers of charges
At a microscopic level, the quantization of charge can't be ignored, as charges can be counted

Charge in Practical Units

A coulomb (C) is a large unit for practical applications
A cubic centimeter of copper contains approximately 2.5 x 10^24 electrons
A cup of water (250 g) contains approximately 8.33 x 10^24 molecules

Coulomb’s Law

Defines the force between two point charges
The force is proportional to the product of the charges and inversely proportional to the square of the distance between them
Force is attractive for opposite charges and repulsive for like charges

Superposition Principle

The total force on a charge due to multiple charges is the vector sum of the forces due to each individual charge

Electric Field

Defined as the force that a unit positive charge would experience if placed at a point in space
The direction of the electric field is the direction of the force on a positive charge
The magnitude of the electric field is independent of the test charge and proportional to the source charge

Examples

An electron falls faster than a proton in a uniform electric field due to its smaller mass
The time of fall for a charged particle in an electric field does not depend on its mass (in contrast to free fall under gravity)
The electric field due to a dipole decreases as the cube of the distance from the center of the dipole on its axis

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Description

This quiz explores the quantization of charge, units of charge, and Coulomb's Law. It also discusses the superposition principle and the concept of electric fields. Test your understanding of these fundamental concepts in electromagnetism.