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Questions and Answers

According to Coulomb's Law, what is the relationship between electrostatic force and the distance between two charges?

  • Inversely proportional to the distance.
  • Directly proportional to the distance.
  • Inversely proportional to the square of the distance. (correct)
  • Directly proportional to the square of the distance.

If the distance between two charges is doubled, how does the electrostatic force between them change?

  • It becomes twice as strong.
  • It becomes half as strong.
  • It becomes four times as strong.
  • It becomes one-fourth as strong. (correct)

What is the value of the electrostatic constant (k) in free space?

  • $6.67 imes 10^{-11} \, ext{Nm}^2/ ext{kg}^2$
  • $9.0 imes 10^8 \, ext{Nm}^2/ ext{C}^2$
  • $9.0 imes 10^9 \, ext{Nm}^2/ ext{C}^2$ (correct)
  • $3.0 imes 10^8 \, ext{m/s}$

Which of the following is analogous to charge in Coulomb's Law, in the context of Newton's Law of Universal Gravitation?

<p>Mass (C)</p> Signup and view all the answers

What is the direction of the electric field defined as?

<p>The direction of force on a positive test charge. (C)</p> Signup and view all the answers

Electric field lines originating from a point charge will point:

<p>Radially outward for a positive charge. (A)</p> Signup and view all the answers

If the magnitude of one of the two charges is doubled, how does the electrostatic force between them change, assuming all other parameters remain constant?

<p>It doubles. (A)</p> Signup and view all the answers

Consider two point charges. If both the magnitudes of the charges are doubled and the distance between them is also doubled, how will the electrostatic force change?

<p>It will remain the same. (C)</p> Signup and view all the answers

Which statement about electric field lines is incorrect?

<p>They can cross each other in regions of strong fields. (A)</p> Signup and view all the answers

What happens to the electric field strength as you move further away from an isolated point charge?

<p>It decreases with the square of the distance. (A)</p> Signup and view all the answers

The electric field strength is defined as:

<p>Force per unit charge. (B)</p> Signup and view all the answers

What is the unit of electric field strength?

<p>Newton per Coulomb (N/C) (D)</p> Signup and view all the answers

Two charges, $+2Q$ and $-Q$, are placed a certain distance apart. Which of the following statements is true regarding the magnitudes of the forces they exert on each other?

<p>They exert equal and opposite forces on each other. (D)</p> Signup and view all the answers

For two like charges, the electric field lines will:

<p>Repel each other and curve away from the region between the charges. (D)</p> Signup and view all the answers

Consider a region with a uniform electric field. If a charge is moved within this field, which path will require the least work to be done against the electric force?

<p>Moving perpendicular to the direction of the electric field. (D)</p> Signup and view all the answers

If charge $Q_1$ is $2 \mu C$ and charge $Q_2$ is $-4 \mu C$ are separated by a distance of $3m$, what is the magnitude of the electrostatic force between them? (Use $k = 9 imes 10^9 , ext{Nm}^2/ ext{C}^2$)

<p>$8 imes 10^{-3} , ext{N}$ (B)</p> Signup and view all the answers

At a certain point in space, an electric field is directed due east and has a magnitude of $100 , ext{N/C}$. What force would be exerted on a proton placed at this point? (Charge of proton $e = 1.6 imes 10^{-19} , ext{C}$)

<p>$1.6 imes 10^{-17} , ext{N}$ East (B)</p> Signup and view all the answers

Two identical positive charges are placed at a distance 'd' apart. At what point on the line joining the two charges is the electric field zero?

<p>Midpoint between the charges. (C)</p> Signup and view all the answers

Three charges $+q$, $+q$, and $+q$ are placed at the vertices of an equilateral triangle. What is the direction of the net electric field at the centroid of the triangle?

<p>The net electric field is zero. (C)</p> Signup and view all the answers

Consider two charges $+Q$ and $-2Q$ separated by a distance $r$. At what distance from the $+Q$ charge, along the line joining the two charges, is the net electric field zero?

<p>Outside the charges, closer to $+Q$. (B)</p> Signup and view all the answers

If the electrostatic force between two charges in a vacuum is $F$, what would be the force between the same two charges when immersed in a medium with a dielectric constant $\kappa$?

<p>$F / \kappa$ (B)</p> Signup and view all the answers

Which of the following scenarios will result in the greatest magnitude of electrostatic force?

<p>Charges of $+2 , ext{C}$ and $-2 , ext{C}$ separated by $2 , ext{m}$. (B)</p> Signup and view all the answers

If a positive test charge is released from rest in an electric field, it will move:

<p>Along the electric field lines towards lower potential. (C)</p> Signup and view all the answers

What is the relationship between the density of electric field lines and the magnitude of the electric field?

<p>Directly proportional. (A)</p> Signup and view all the answers

Which of the following is a vector quantity?

<p>Electric field strength (D)</p> Signup and view all the answers

Compared to gravitational forces, electrostatic forces are generally:

<p>Much stronger. (B)</p> Signup and view all the answers

Which of the following is true about the electrostatic force and the gravitational force?

<p>Electrostatic force can be attractive or repulsive, and gravitational force is always attractive. (D)</p> Signup and view all the answers

Imagine a scenario where Coulomb's constant $k$ was suddenly doubled. How would this affect the electrostatic force between two charges?

<p>The force would be doubled. (A)</p> Signup and view all the answers

If the distance between two charges is reduced to half its original value, the electrostatic force between them becomes:

<p>Four times the original force. (D)</p> Signup and view all the answers

In a region where the electric field lines are parallel and equally spaced, what can be concluded about the electric field?

<p>The electric field is uniform and constant in magnitude and direction. (C)</p> Signup and view all the answers

A proton and an electron are placed in a uniform electric field. Which of the following statements is true?

<p>They experience forces of equal magnitude and in opposite directions. (B)</p> Signup and view all the answers

What is the effect on electrostatic force if the distance between two charges is tripled?

<p>Decreases by a factor of nine (D)</p> Signup and view all the answers

If both the magnitudes of two charges are halved, and the distance between them remains constant, how does the electrostatic force change?

<p>Is reduced to one-quarter of its original value (B)</p> Signup and view all the answers

In Coulomb's Law, what does the constant ( k ) represent?

<p>Electrostatic constant (D)</p> Signup and view all the answers

Which of the following is most analogous to mass in Newton's Law of Universal Gravitation, within the framework of Coulomb's Law?

<p>Charge (A)</p> Signup and view all the answers

The direction of an electric field is defined as the direction of the force on what type of charge?

<p>A positive charge (D)</p> Signup and view all the answers

Electric field lines near a negative point charge will:

<p>Point towards the charge (B)</p> Signup and view all the answers

Increasing the magnitude of one of the two charges has what effect on the electrostatic force, all other parameters being constant?

<p>Increases the force (B)</p> Signup and view all the answers

If both charges are tripled and the distance between them is halved, how will the electrostatic force change?

<p>Increase by a factor of 36 (B)</p> Signup and view all the answers

Which statement is correct regarding electric field lines?

<p>Their density indicates the strength of the electric field (D)</p> Signup and view all the answers

How does the electric field strength change as you move closer to an isolated point charge?

<p>Increases exponentially (C)</p> Signup and view all the answers

Two charges, $-3Q$ and $+Q$, are positioned at a distance. Which statement is correct about the forces they exert on each other?

<p>The forces are equal in magnitude but opposite in direction (D)</p> Signup and view all the answers

Electric field lines for two unlike charges will:

<p>Originate from the positive charge and terminate on the negative charge (D)</p> Signup and view all the answers

Within a uniform electric field, which path requires the most work to move a charge against the electric force?

<p>A path parallel to the field lines (B)</p> Signup and view all the answers

Two charges of $+6 \mu C$ and $-2 \mu C$ are separated by $6m$. Calculate the electrostatic force between them, using $k = 9 imes 10^9 , ext{Nm}^2/ ext{C}^2$.

<p>$0.003 N$ (D)</p> Signup and view all the answers

An electric field of $500 , ext{N/C}$ is directed due north. What force would be exerted on an electron placed in this field? (Charge of electron $e = -1.6 imes 10^{-19} , ext{C}$)

<p>$8.0 imes 10^{-17} , ext{N}$ South (A)</p> Signup and view all the answers

Two identical negative charges are separated by a distance '2d'. Determine the location where a positive test charge would experience the maximum electric field strength.

<p>At either of the locations of the negative charges (B)</p> Signup and view all the answers

Three charges, $-2q$, $+q$, and $+q$, are placed at the vertices of an equilateral triangle. Determine the direction of the net electric field at the centroid of the triangle.

<p>Toward the $-2q$ charge (B)</p> Signup and view all the answers

Two charges, $+4Q$ and $-Q$, are separated by a distance $r$. Find the point along the line joining them where the net electric field is zero.

<p>2r from the +4Q charge (C)</p> Signup and view all the answers

If the electrostatic force between two charges in a medium is $F'$ and the force in a vacuum is $F$, and given the dielectric constant of the medium is $\kappa$ = 5, what is the relationship between $F'$ and $F$?

<p>$F' = F/5$ (B)</p> Signup and view all the answers

Which scenario results in the smallest magnitude of electrostatic force?

<p>Charges of $+2Q$ and $+2Q$ separated by a distance of $2r$ (D)</p> Signup and view all the answers

If a negative test charge is released from rest in an electric field, in what direction will it move?

<p>Opposite to the direction of the electric field (A)</p> Signup and view all the answers

What does the spacing of electric field lines indicate about the magnitude of the electric field?

<p>The magnitude is stronger where the lines are closer together (C)</p> Signup and view all the answers

Compared to electrostatic forces, gravitational forces are generally:

<p>Much weaker (A)</p> Signup and view all the answers

Which of the following statements accurately compares electrostatic force and gravitational force?

<p>Electrostatic force can be attractive or repulsive, while gravitational force is only attractive (D)</p> Signup and view all the answers

If Coulomb's constant (k) were suddenly halved, how would this affect the electrostatic force between two charges?

<p>The force would be halved (C)</p> Signup and view all the answers

If the distance between two charges is increased by a factor of four, the electrostatic force between them is:

<p>Decreased by a factor of 16 (A)</p> Signup and view all the answers

In a region where the electric field lines converge, what can be concluded about the electric field?

<p>The electric field is increasing in strength (A)</p> Signup and view all the answers

A proton and an electron are released from rest in a uniform electric field. Which statement is true regarding their acceleration?

<p>They accelerate in opposite directions, with the electron's acceleration having a greater magnitude (B)</p> Signup and view all the answers

Flashcards

Coulomb's Law

The electrostatic force between two point-like charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges.

Electrostatic Constant (k)

A fundamental constant that appears in electrostatics. It is approximately equal to 9.0 x 10^9 N⋅m²/C².

Electric Field

A region of space in which an electric charge will experience a force.

Electric Field Lines

Lines that represent the direction and strength of an electric field. They point away from positive charges and towards negative charges.

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Electric Field Strength (E)

The force per unit charge that a test charge would experience at a given point in space.

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Positive Test Charge

A small, positive charge used to test the electric field in a given space. It's theoretical, with a charge of +q.

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Charge Interaction

The principle that like charges repel each other, while unlike charges attract each other.

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Electrostatic Force

The magnitude of attraction or repulsion between two charged objects.

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Coulomb's Law Formula

An expression of the electrostatic force (F) between two charges (Q1, Q2) separated by a distance (r), involving the electrostatic constant (k).

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Electrostatic Constant Value

Constant appearing in Coulomb's Law denoted as k, approximately equal to 9.0 x 10^9 N⋅m²/C² in free space.

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Non-Contact Forces

Charges exert influence on each other without direct contact.

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Electric Field Lines Purpose

A tool to visualize the direction and strength of an electric field.

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Field Lines Around Positive Charge

Points away from the charge, indicating repulsion of a positive test charge.

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Field Lines Around Negative Charge

Points towards the charge, indicating attraction of a positive test charge.

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Field Lines: Unlike Charges

Lines start from positive and end at negative charges, showing attraction.

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Field Lines: Like Charges

Lines repel each other, creating a zone of zero net force in the middle.

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Unequal Charge Magnitudes

The field is stronger around the charge with greater magnitude.

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Electric Field Strength Formula

Expressed as E = F/q, measured in newtons per coulomb (N/C).

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Electric Field Strength Formula (Coulomb)

An alternative to E = F/q, emphasizing dependence on source charge (Q) and distance (r).

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Study Notes

Coulomb’s Law

  • Like charges repel each other, while unlike charges attract each other
  • Electrostatic force occurs when the charges are at rest
  • The magnitude of the electrostatic force increases with the magnitude of the charges
  • The magnitude of the electrostatic force decreases as the distance between the charges increases
  • Charles-Augustin de Coulomb detailed electrostatic force around 1784
  • The magnitude of the electrostatic force between two point-like charges is inversely proportional to the square of the distance between the charges
  • The magnitude of the force is proportional to the product of the charges

Coulomb's Law Formula

  • F ∝ (Q1Q2)/r² where Q1 and Q2 are magnitudes of two charges and r is the distance between them
  • F = k (Q1Q2)/r² where k is the electrostatic constant
  • Electrostatic constant (k) value is 9.0 x 10^9 Nm²/C² in free space
  • Newton’s universal law of gravitation formula: FG = G (m1m2)/d² where m1 and m2 are masses of two particles, d is the distance between them and G is the gravitational constant
  • Electrostatic force (F) is proportional to the product of magnitudes of the charges
  • Electrostatic force (F) is inversely proportional to the square of the distance between them
  • As the distance between charges doubles, the electrostatic force decreases by a factor of four
  • Coulomb’s law is similar in form to Newton’s universal law of gravitation; both are inverse-square laws.
  • Both laws represent the force exerted by particles (point masses or point charges) on each other that interact by means of a field

Electric Field

  • Electric field is a region of space where an electric charge experiences a force
  • The direction of the electric field at any point is the direction of the force that a positive test charge would experience at that point

Representing Electric Fields

  • Electric field lines represent the strength and direction of an electric field
  • Electric field lines show the direction a positive test charge would move if placed in the field
  • Electric field lines are drawn to represent the force experienced by a test charge at various points around a source charge
  • Around a positive charge (+Q), a positive test charge (+q) will experience a repulsive force
  • The force that a test charge experiences is governed by Coulomb’s law

Positive and Negative Charges

  • Force vectors at different points around the positive charge are arrows that point away from the charge
  • Force decreases with distance
  • For a negative charge (Q), a positive test charge (+q) will experience an attractive force
  • Force vectors point towards the negative charge
  • The magnitude of the force is the same at the same distances as in the case of a positive charge
  • The direction is opposite due to the attractive nature of the interaction between opposite charges

Conventions

  • Arrows on field lines indicate field direction
  • Field lines point away from positive charges and towards negative charges
  • Field lines are closer together where the field is stronger
  • Field lines do not touch or cross each other
  • Field lines are drawn perpendicular to a charge or charged surface
  • The greater the magnitude of the charge, the stronger its electric field, represented by more field lines around the charge

Electric Fields Around Different Charge Configurations

  • For a positive and a negative charge placed next to each other, electric field lines start from the positive charge and end at the negative charge
  • For two positive charges of equal magnitude placed next to each other, electric field lines repel from both charges
  • Two positive charges create a region where electric fields cancel out so there is no net force
  • The electric field around two negative charges is similar in structure to that around two positive charges but with the direction of the field lines reversed
  • When the magnitudes of the charges are different, the field lines are more influenced by the charge with the greater magnitude
  • Results in a field configuration where the field lines are more densely packed around the stronger charge indicating a stronger electric field in that region

Electric Field Strength

  • Electric field strength at a point is the force per unit charge that a test charge would experience at that point
  • E = F/q where F is the force experienced by a test charge q
  • Units of electric field strength are newtons per coulomb (N/C)
  • E = kQ/r² where Q is the source charge creating the electric field, r is the distance from the source charge to the point where the field strength is being calculated, and k is Coulomb’s constant (9.0 × 10^9 Nm²/C²)

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