Electrostatics Problem: Force between Charged Spheres

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Questions and Answers

Two charged spheres are kept at a finite centre-to-centre spacing. If the calculated force of electrostatic interaction is Fc and the measured force is Fm, which conclusion is correct?

Irrespective of their materials, Fc > Fm for like charges and Fc < Fm for unlike charges. (correct)

If Fc > Fm for like charges and Fc < Fm for unlike charges, both the spheres must be made of insulating materials.

Irrespective of their materials, Fc < Fm for like charges and Fc > Fm for unlike charges.

If Fc > Fm for like charges and Fc < Fm for unlike charges, both the spheres must be made of conducting materials.

How much maximum charge can a thin conducting ring be given without rupturing compared to another ring with a different radius and tensile strength?

Insufficient information

< qnk

< qn√k (correct)

< qn^2 √k

In which figure or figures can the illustrated electric field be created by a single point charge at points A and B?

None of the figures

Figure c

Figure a (correct)

Figures a and c (correct)

On a hemispherical frictionless dome in a uniform horizontal electric field, if a positively charged disc leaves after an angular displacement 𝜃 = sin⁡(3/5), what is the ratio of gravitational and electrostatic forces on the disc?

9/2 Signup and view all the answers

Which figure best represents electric field lines between two infinitely large planes A and B carrying uniform surface charge densities +𝜎 and −𝜎?

Figure b Signup and view all the answers

Which of the following figures show incorrect representations of electric field lines?

Figure b Signup and view all the answers

In the given electric field line configuration, if q1 = 1μC, the charge q2 is closest to

−8μC Signup and view all the answers

For a conducting shell of radius R with charge Q, what is the electrostatic force between two parts of the shell on either side of a plane at distance r(< R) from the center?

32πε0 Q²r² / (1 - R²) Signup and view all the answers

In an alternative world with a different electric force law, what statements are true regarding the electric field?

Electric field due to a point charge Q is E = 4πε₀Q(1−√αr) / r³ Signup and view all the answers

In a region of free space with a uniform electric field pointed along a chain, what is the magnitude of induced charges on one end ball of a straight chain?

2πε₀ r(n − 1)lE Signup and view all the answers

If two identical point charges have equal velocity vectors making certain angles and their total kinetic energy is equal to their potential energy, what is the distance of closest approach between them?

40 cm Signup and view all the answers

For a charge particle at an angle β from a uniform slope of inclination α, what is the maximum value of β for equilibrium if the coefficient of friction is μ (μ < tan⁡ α)?

sin⁻¹(μcot⁡ α) Signup and view all the answers

For a rod with a negatively charged small ball at one end and a positively charged ball at a fixed height above, what is the range of values for the mass of the lower ball to maintain stable equilibrium?

m > 4πε₀ qQ / g(h+l) Signup and view all the answers

When a conducting frame is rotated in a uniform electric field, what are the charges induced on the rods if total charges initially on DC and OC are q1 and q2 respectively?

The charges induced on each rod are proportional to their distances from the corner A towards corner D. Signup and view all the answers

Study Notes

Electrostatics

Force of Electrostatic Interaction

Two charged spheres are kept at a finite centre-to-centre spacing, and the force of electrostatic interaction between them is calculated.
If the calculated force (Fc) is greater than the measured force (Fm) for like charges, and Fc is less than Fm for unlike charges, both spheres must be made of conducting materials.
If the calculated and measured forces are equal, regardless of the material, Fc is less than Fm for like charges and Fc is greater than Fm for unlike charges.

Rupture of a Thin Conducting Ring

A thin conducting ring is ruptured when it is given a charge q.
If the radius of another ring is n times the former ring and the tensile strength is k times, the maximum charge the second ring can be given without rupturing is less than qn√k.

Electric Field Vectors

Electric field vectors at two points A and B in an electric field can be created by a single point charge.
The illustrated field can be created by a single point charge in figures (a) and (c).

Electric Field and Gravitational Forces

A positively charged small disc is released on the top of a fixed hemispherical frictionless dome in a uniform horizontal electric field.
If the disc leaves the dome after an angular displacement θ = sin⁻¹(3/5), the ratio of gravitational and electrostatic forces on the disc is 9/2.

Electric Field Lines

Two infinitely large planes A and B intersect each other at right angles and carry uniform surface charge densities +σ and -σ.
The electric field lines are best represented in figure (b).

Incorrect Representations of Electric Field Lines

Figures (a), (b), and (c) are incorrect representations of electric field lines.

Electric Field Created by Two Point Charges

The electric field created by two point charges q1 and q2 is shown in the figure.
If q1 = 1μC, the charge q2 is closest to -8μC.

Electrostatic Force between Two Parts of a Conducting Shell

A conducting shell of radius R has a charge Q.
The electrostatic force between two parts of the shell, which are on either sides of a plane that is at a distance r (r < R) from the centre of the shell, is given by the expression: Q² / (32πε₀ r² (1 - R²)).

Alternative Electric Force Law

In another world, the electric force F on a point-like charge q due to another point-like charge Q is given by the law: F = Qq(1 - √αr) / (4πε₀ r³).
The electric field due to a point charge Q is E = Q(1 - √αr) / (4πε₀ r³).
The line integral of this electric field over a closed path is also zero, as in our world.
Gauss' law ∮E⋅ds = qenclosed / ε₀ also holds true for this electric field.

Induced Charges on a Metal Ball

A straight chain consisting of n identical metal balls is at rest in a region of free space.
A uniform electric field E is switched on in the region.
The magnitude of the induced charges on one of the end balls is 2πε₀r(n-1)lE.

Distance of Closest Approach between Two Point Charges

Two identical point charges are moving in free space, when they are 60 cm apart.
Their velocity vectors are equal in modulus and make angles of 45° from the line joining them.
If at this instant, their total kinetic energy is equal to their potential energy, the distance of closest approach between them is 40 cm.

Equilibrium of a Charge Particle on a Slope

A charge particle A is fixed at the base of a uniform slope of inclination α.
Another charge particle B is placed on the slope at an angular position β from the line of greatest slope through the position of the first particle.
The coefficient of friction between the particle B and the slope is μ (μ < tanα).
For the particle at B to stay in equilibrium, the maximum value of the angle β is sin⁻¹(μcotα).

Stable Equilibrium of a Charged Rod

One end of an insulating rigid rod of negligible mass and length l is pivoted to a fixed point O.
A small ball of mass m having a negative charge of modulus q is attached to the lower end of the rod.
Another small ball carrying a positive charge Q is fixed at a height h above the point O.
The range of values of mass m of the lower ball for the rod to remain in a state of stable equilibrium is m > 4πε₀gh / (h+l).

Charges Induced on a Conducting Frame

A rigid frame in the shape of a right pyramid is made of conducting rods.
The base ABCD is a square and the apex O is vertically above the centre of the base.
The frame is electrically neutral.
When it is placed in a uniform electric field of intensity E pointing from the corner A towards the corner D, total charges induced on the rods DC and OC are known to be q1 and q2 respectively.
If the frame is rotated to make the electric field pointing from the corner A towards the corner C, the charges induced on each rod are proportional to their distances from the corner.

Electric Field at the Centre of a Cube

Three identical thin uniformly charged filaments are fixed along three sides of a cube.
Length of each filament is l and line charge density on each of them is λ.
The electric field at the centre of the cube is zero.

Acceleration of a Disc on a Triangular Prism

In presence of a uniform horizontal electric field E, a small non-conducting disc of mass m and charge q is released on a non-conducting triangular prism of mass M placed on a frictionless horizontal floor.
Slant face of the prism makes an angle θ with the horizontal and coefficient of friction between it and the disc is μ.
If the disc accelerates up the slant face, the acceleration of the prism is (qEsinθ+mgcosθ) / (M+msinθ)⋅(sinθ+μcosθ).

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Description

Solve a physics problem involving the calculation and measurement of electrostatic force between two charged spheres. Applies to electrostatics chapter in physics.