Electric Charges and Fields Quiz
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Questions and Answers

What is the formula for the magnetic field at the center of a circular arc carrying a current?

  • µ0 Iφ / 4πr (correct)
  • µ0 I sin θ / 4πr2
  • µ0 I / 4πr
  • µ0 I / 2r

    • What is the formula for the resistance of a conductor at temperature t°C?

  • Rt = R0 (1 + at)
  • Rt = R0 + at + bt2
  • Rt = R0 (1 + at + bt2) (correct)
  • Rt = R0 / (1 + at)

    • What is the formula for the magnetic field at a point on the axis of a circular current-carrying coil?

  • B = µ0 I / 2r
  • B = µ0 Iφ / 4πr
  • B = µ0 2πNIa2 / 4π(a2 + x2)3/2 (correct)
  • B = µ0 I sin θ / 4πr2

    • What is the formula for the torque on a current-carrying coil placed in a magnetic field?

    <p>t = NIAB cos θ (B)</p> Signup and view all the answers

    What is the formula for the magnetic field at a point due to a straight wire of finite length carrying current I at a perpendicular distance r?

    <p>B = µ0 I [sin α + sin β] / 4πr (A)</p> Signup and view all the answers

    What is the formula for the work done in rotating a coil through an angle θ from the field direction?

    <p>W = MB (1 – cos θ) (D)</p> Signup and view all the answers

    What is the formula for the potential energy of a magnetic dipole in a magnetic field?

    <p>U = -MB cos θ (A)</p> Signup and view all the answers

    What is the relationship between current density (J), conductivity (s), and electric field (E)?

    <p>J = sE (C)</p> Signup and view all the answers

    What is the formula for the distance of the nth bright fringe from the center in a double slit experiment?

    <p>$x_n = n \lambda$ (B)</p> Signup and view all the answers

    In the context of forming dark fringes in a double slit experiment, what is the path difference for the nth dark fringe?

    <p>$\frac{(2n - 1)\lambda}{2}$ (B)</p> Signup and view all the answers

    Which of the following describes the meaning of 'dispersive power' in optics?

    <p>The angular separation of different colors (D)</p> Signup and view all the answers

    What is the magnifying power (M) formula of a simple microscope when the image is formed at infinity?

    <p>$M = \frac{\tan \beta}{\tan \alpha}$ (A)</p> Signup and view all the answers

    In the context of a double slit experiment, what does the variable 'd' represent?

    <p>Distance between two slits (B)</p> Signup and view all the answers

    What happens to the number of images formed when the object is in a denser medium?

    <p>It depends on whether the number is odd or even. (D)</p> Signup and view all the answers

    What is the lens maker's formula used for?

    <p>To find the focal length of a lens based on its radii. (A)</p> Signup and view all the answers

    Which formula represents the thin lens formula?

    <p>$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ (B)</p> Signup and view all the answers

    How is the linear magnification represented mathematically?

    <p>$m = \frac{v}{u}$ (C)</p> Signup and view all the answers

    What does positive Power (P) of a lens indicate?

    <p>The lens is convex. (D)</p> Signup and view all the answers

    What does the formula for longitudinal magnification represent?

    <p>The change in object size with distance. (C)</p> Signup and view all the answers

    What does the symbol ρ represent in the resistance formula R = ρ * (l/A)?

    <p>Resistivity of the conductor (D)</p> Signup and view all the answers

    If the focal length (f) is negative, what does this indicate about the lens?

    <p>The lens is a diverging lens. (C)</p> Signup and view all the answers

    In the context of conductivity, what is the equation representing conductivity σ?

    <p>σ = ne / ρ (C)</p> Signup and view all the answers

    What is the relationship between the combined power of lenses in contact?

    <p>The individual powers simply add up. (A)</p> Signup and view all the answers

    What expression represents the force on a charged particle in a magnetic field?

    <p>F = qvB sin θ (A)</p> Signup and view all the answers

    What does the angular frequency formula for a charged particle indicate?

    <p>ω = qB / m (B)</p> Signup and view all the answers

    What is the formula for the resistance of a cylindrical tube with inner radius r1 and outer radius r2?

    <p>R = ρ * l / (π(r2² - r1²)) (C)</p> Signup and view all the answers

    What does the time period of revolution T depend on for a charged particle in a uniform magnetic field?

    <p>T = 2πm/qB (A)</p> Signup and view all the answers

    Which formula describes the frequency of a charged particle's motion in a magnetic field?

    <p>ν = qB / 2πm (A)</p> Signup and view all the answers

    What is the relationship between electric field strength E and the force on a charged particle?

    <p>F = qE (C)</p> Signup and view all the answers

    What is the de Broglie wavelength of a gas molecule at temperature T?

    <p>$\frac{h}{3mkT}$ (C)</p> Signup and view all the answers

    What does the Angular fringe width of secondary maxima or minima depend on?

    <p>$\frac{\lambda}{a}$ (B)</p> Signup and view all the answers

    Which formula correctly represents the resolving power of a microscope?

    <p>$\frac{1}{2\mu \sin\theta}$ (B)</p> Signup and view all the answers

    When considering the resolving power of a telescope, which variable significantly affects it?

    <p>Total aperture D (C)</p> Signup and view all the answers

    What is the energy of a photon expressed in terms of frequency?

    <p>$E = h\nu$ (B)</p> Signup and view all the answers

    In relation to scattering, how is the impact parameter b defined?

    <p>$b = Ze^2 \cot(\theta/2)$ (B)</p> Signup and view all the answers

    Which equation represents the relation of momentum of a photon?

    <p>$p = \frac{E}{c}$ (D)</p> Signup and view all the answers

    How is the frequency of incident alpha particles related to the impact parameter?

    <p>$f = \pi n_t \left(\frac{Ze^2}{4\pi\epsilon K}\right)\cot^2(\theta/2)$ (B)</p> Signup and view all the answers

    What is the formula for the frequency of an electron in the nth orbit?

    <p>$\frac{4 \pi^2 Z^2 e^4 m}{n^3 h^3}$ (D)</p> Signup and view all the answers

    How is the wavelength of radiation in the transition from n2 to n1 expressed?

    <p>$RZ^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$ (B)</p> Signup and view all the answers

    What does the term 'ionization energy' refer to in the given context?

    <p>The energy required to remove an electron from an atom completely. (C)</p> Signup and view all the answers

    What is the formula for calculating the number of spectral lines due to electron transitions?

    <p>$n(n - 1)$ (C)</p> Signup and view all the answers

    In the context of the Lyman series, what transitions does it involve?

    <p>From higher levels to n1 = 1. (A)</p> Signup and view all the answers

    What is the expression for the energy quantization of an electron in the nth orbit?

    <p>$E_n = \frac{Z^2}{n^2} \times 13.6 eV$ (D)</p> Signup and view all the answers

    What constant is used to determine the nuclear radius?

    <p>(R_0) (C)</p> Signup and view all the answers

    What is the relationship between the ionization potential and the atomic number Z?

    <p>Ionization potential increases with Z squared. (C)</p> Signup and view all the answers

    Study Notes

    Electric Charges and Fields

    • Coulomb's law: F = kq₁q₂/r²
    • Relative permittivity (dielectric constant): εr or K = ε/ε₀
    • Electric field intensity at a point distant r from a point charge q: E = 1/(4πε₀r²) q
    • Electric dipole moment: p = qd
    • Electric field intensity on axial line (end-on position) of the dipole:
      • At distance r from the centre: E = 1/(2πε₀r³) p
      • At large distance (r >> a): E = 1/(4πε₀r²) p
    • Electric field intensity on equatorial line (broadside position) of the dipole:
      • At distance r from the centre: E = 1/(4πε₀ (r² + a²)³/²) p
      • At large distance (r >> a): E = 1/(4πε₀r³) p
    • Electric field intensity at any point due to an electric dipole: E = (1/4πε₀r³) √(1 + 3cos²θ) p
    • Electric field intensity due to a charged ring:
      • At a point on its axis at a distance r from its centre: E = 1/(4πε₀(r² + a²)³/²) q
    • Electric field due to thin infinitely long straight wire of uniform linear charge density λ:
      • At a point outside the shell (r > R): E = λ/(2πε₀r)
    • Electric field due to a non-conducting solid sphere of uniform volume charge density ρ and radius R at a point:
      • Outside the sphere (r > R): E = (1/4πε₀r²) Q
      • On the surface of the sphere (r = R): E = (1/4πε₀R²) Q
      • Inside the sphere (r < R): E = (1/3ε₀R³) ρr

    Electrostatic Potential and Capacitance

    • Electric potential V = W/q
    • Electric potential at a point distant r from a point charge q: V = q/(4πε₀r)
    • Electric potential at a point due to an electric dipole: V = (1/4πε₀r²) p cos θ
    • Relationship between E and V: E = -dV/dr
    • Capacitance of a spherical conductor of radius R: C = 4πε₀R
    • Capacitance of an air filled parallel plate capacitor: C = ε₀A/d
    • Capacitance of an air filled spherical capacitor: C = 4πε₀ab/(b-a)
    • Capacitance of an air filled cylindrical capacitor: C = 2πε₀L/ln(b/a)
    • Electric potential due to a uniformly charged spherical shell:
      • Outside the shell (r > R): V = Q/(4πε₀r)
      • On the shell (r = R): V = Q/(4πε₀R)
      • Inside the shell (r < R): V = Q/(4πε₀R)
    • Electric potential due to a non-conducting solid sphere:
      • Outside the sphere (r > R): V = Q/(4πε₀r)
      • On the sphere (r = R): V = Q/(4πε₀R)
      • Inside the sphere (r < R): V = Q/8πε₀R(3R²-r²)/R³

    Current Electricity

    • Current: I = Q/t
    • Current density: J = I/A
    • Drift velocity: vd = (eEτ)/(m)
    • Relationship between current and drift velocity: I = nAved
    • Relationship between current density and drift velocity: J = nevd
    • Mobility: μ = vd/E
    • Conductance: G = 1/R
    • Resistance of a conductor: R = ρL/A
    • Conductivity: σ = 1/ρ
    • Resistance of a conductor in the form of a wire of length L and radius r: R = ρL/(πr²)
    • Relationship between J, σ and E: J = σE

    Moving Charges and Magnetism

    • Force on a charged particle in a uniform electric field: F = qE
    • Force on a charged particle in a uniform magnetic field: F = q(v × B) or qvBsinθ
    • Radius of circular path: R = mv/(qB)
    • Time period of revolution: T = 2πm/(qB)
    • Cyclotron frequency: ν = qB/(2πm)

    Magnetism and Matter

    • Gauss's law for magnetism: ΣB.ΔS = 0
    • Magnetic intensity: B = μH
    • Intensity of magnetization: I = M/V
    • Magnetic susceptibility: χm = (M/H)
    • Magnetic permeability: μ = B/H
    • Relative permeability: μr = μ/μ₀

    Electromagnetic Induction

    • Magnetic flux: Φ = B.A cos θ
    • Faraday's law of electromagnetic induction: ε = -dΦ/dt
    • Self-induced emf: ε = -L(dI/dt)
    • Self inductance of a circular coil: L = μ₀N²A/l

    Alternating Current

    • Average value of alternating current over a complete cycle: Iav = 0
    • Root mean square (rms) value of alternating current: Irms= I0/√2
    • Quality factor: Q = ω0L/R = 1/(R√C)
    • Form factor = Irms/Iav = 1.11 (for half wave rectifier), 1.21 (full wave rectifier)

    Wave Optics

    • For constructive interference (bright fringes) : d sin θ = nλ
    • For destructive interference (dark fringes) : d sin θ = (2n - 1)λ / 2
    • Fringe width: β = λD/d
    • Angular fringe width: θ = λ/d

    Ray Optics and Optical Instruments

    • Mirror's formula: 1/f = 1/v + 1/u
    • Lens maker's formula: 1/f = (μ-1)(1/R1-1/R2)
    • Thin lens formula: 1/f = 1/v-1/u
    • Linear magnification : m = v/u
    • Power of a lens: P = 1/f (in dioptres)
    • Length of telescope tube: L= f₀+fe

    Atoms

    • Bohr's radius: rₙ = (n²h²)/(4π²me²Z)
    • Velocity of electron in the nth orbit (vn) = (2πZe²)/(4πε₀nh)
    • Kinetic energy of electron: Kn = (1/2)mvn²
    • Potential energy of electron: Un = -2πZe²/4πε₀n = -2πZe²/4πε₀n
    • Total energy of electron: En = Kn + Un
    • Balmer series: (1/λ)=R[ 1/(n2)^2 - 1/(n1)^2]

    Communication System

    • Maximum line of sight distance: dmax ~ √2h1h2 + R.
    • Critical frequency, Maximum usable frequency (MUF)= v=(Nmax) ^1/2

    Semiconductor Electronics

    • Current in a junction diode: I = Ioe(eV/kT - 1)

    Other

    • Mass defect: ∆m = (Σmi - mnuc)
    • Binding energy per nucleon: Eb/A = ∆mc2/A

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    Description

    Test your understanding of electric charges and fields with this quiz. It covers key concepts including Coulomb's law, electric field intensity, and the behavior of electric dipoles. Challenge yourself with problems that apply these fundamental principles of physics.

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