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Questions and Answers
A spherical capacitor has inner and outer radii of 'a' and 'b' respectively. If the inner sphere is grounded, what is the capacitance of the capacitor?
A spherical capacitor has inner and outer radii of 'a' and 'b' respectively. If the inner sphere is grounded, what is the capacitance of the capacitor?
- $4\pi \epsilon_0 b$
- $4\pi\epsilon_0 \frac{ab}{b-a}$
- $4\pi \epsilon_0 a$ (correct)
- $\frac{4\pi \epsilon_0}{a}$
A copper wire has a length $L$ and cross-sectional area $A$. If the length of the wire is doubled and the cross-sectional area is halved, how does the resistance change?
A copper wire has a length $L$ and cross-sectional area $A$. If the length of the wire is doubled and the cross-sectional area is halved, how does the resistance change?
- The resistance is halved.
- The resistance is doubled.
- The resistance is quadrupled. (correct)
- The resistance remains the same.
An electrical cell has an EMF 'E' and internal resistance 'r'. When connected to an external resistance 'R', what is the terminal potential difference 'V' across the cell?
An electrical cell has an EMF 'E' and internal resistance 'r'. When connected to an external resistance 'R', what is the terminal potential difference 'V' across the cell?
- $V = E + Ir$
- $V = E - Ir$ (correct)
- $V = IR$
- $V = E$
In a Wheatstone bridge circuit, the ratio of resistances in the first two arms is $\frac{P}{Q}$. For the bridge to be balanced, what must be the ratio of resistances in the other two arms, $\frac{R}{S}$?
In a Wheatstone bridge circuit, the ratio of resistances in the first two arms is $\frac{P}{Q}$. For the bridge to be balanced, what must be the ratio of resistances in the other two arms, $\frac{R}{S}$?
A charged particle with charge 'q' moves with velocity $\overrightarrow{V}$ in a magnetic field $\overrightarrow{B}$. What is the magnetic force $\overrightarrow{F}$ acting on the particle?
A charged particle with charge 'q' moves with velocity $\overrightarrow{V}$ in a magnetic field $\overrightarrow{B}$. What is the magnetic force $\overrightarrow{F}$ acting on the particle?
A wire carries a current $I$. According to Biot-Savart law, what is the magnetic field $dB$ at a distance $r$ from a small element $dl$ of the wire, where the angle between the current element and the line joining the element to the point is $\theta$?
A wire carries a current $I$. According to Biot-Savart law, what is the magnetic field $dB$ at a distance $r$ from a small element $dl$ of the wire, where the angle between the current element and the line joining the element to the point is $\theta$?
Two parallel wires carry currents $I_1$ and $I_2$ separated by a distance $r$. What is the force per unit length $l$ between the wires?
Two parallel wires carry currents $I_1$ and $I_2$ separated by a distance $r$. What is the force per unit length $l$ between the wires?
What happens to the drift velocity of electrons in a metallic conductor when the temperature of the conductor increases?
What happens to the drift velocity of electrons in a metallic conductor when the temperature of the conductor increases?
A circular coil of radius a is carrying current i. What is the magnetic field B at a point on its axis, a distance x from the center?
A circular coil of radius a is carrying current i. What is the magnetic field B at a point on its axis, a distance x from the center?
A long, straight wire of radius a carries a current i. According to Ampere's law, what is the magnetic field B at a distance r from the center of the wire when r < a?
A long, straight wire of radius a carries a current i. According to Ampere's law, what is the magnetic field B at a distance r from the center of the wire when r < a?
A galvanometer with coil resistance $R_G$ needs to be converted into an ammeter to measure current up to I amperes. If the galvanometer's full-scale deflection current is $I_g$, what shunt resistance R is required?
A galvanometer with coil resistance $R_G$ needs to be converted into an ammeter to measure current up to I amperes. If the galvanometer's full-scale deflection current is $I_g$, what shunt resistance R is required?
A solenoid with n turns per unit length carries a current i. What is the magnetic field strength $B_s$ inside the solenoid, assuming the core material has permeability $\mu$?
A solenoid with n turns per unit length carries a current i. What is the magnetic field strength $B_s$ inside the solenoid, assuming the core material has permeability $\mu$?
The magnetic potential energy of a magnetic dipole in a uniform magnetic field is given by $U = -M \cdot B$. If the dipole moment is $M = 5 , \text{A m}^2$ and the magnetic field is $B = 2 , \text{T}$, what is the potential energy when the dipole is aligned anti-parallel to the field?
The magnetic potential energy of a magnetic dipole in a uniform magnetic field is given by $U = -M \cdot B$. If the dipole moment is $M = 5 , \text{A m}^2$ and the magnetic field is $B = 2 , \text{T}$, what is the potential energy when the dipole is aligned anti-parallel to the field?
In an alternating current (AC) circuit, the RMS voltage is related to the peak voltage. If the peak voltage is $V_0$, what is the RMS voltage $V_{rms}$?
In an alternating current (AC) circuit, the RMS voltage is related to the peak voltage. If the peak voltage is $V_0$, what is the RMS voltage $V_{rms}$?
An object is placed in front of a concave mirror. If the object distance is u, the image distance is v, and the focal length of the mirror is f, which of the following equations correctly relates these quantities?
An object is placed in front of a concave mirror. If the object distance is u, the image distance is v, and the focal length of the mirror is f, which of the following equations correctly relates these quantities?
A point charge q is placed at a distance r from an infinite, non-conducting sheet with uniform surface charge density $\sigma$. What is the force on the charge q?
A point charge q is placed at a distance r from an infinite, non-conducting sheet with uniform surface charge density $\sigma$. What is the force on the charge q?
In a Young's double-slit experiment, the intensity at a point on the screen where the path difference is zero is $I_{max}$. If one of the slits is closed, what will be the intensity at the same point?
In a Young's double-slit experiment, the intensity at a point on the screen where the path difference is zero is $I_{max}$. If one of the slits is closed, what will be the intensity at the same point?
Two capacitors with capacitances $C_1$ and $C_2$ are connected in series. What is the equivalent capacitance of the combination?
Two capacitors with capacitances $C_1$ and $C_2$ are connected in series. What is the equivalent capacitance of the combination?
A parallel plate capacitor is charged and then disconnected from the battery. If the distance between the plates is increased, what happens to the electric potential difference between the plates?
A parallel plate capacitor is charged and then disconnected from the battery. If the distance between the plates is increased, what happens to the electric potential difference between the plates?
A dipole with dipole moment $\overrightarrow{p}$ is placed in a uniform electric field $\overrightarrow{E}$. Which of the following statements is correct regarding the torque ($\overrightarrow{\tau}$) and potential energy (U) of the dipole?
A dipole with dipole moment $\overrightarrow{p}$ is placed in a uniform electric field $\overrightarrow{E}$. Which of the following statements is correct regarding the torque ($\overrightarrow{\tau}$) and potential energy (U) of the dipole?
What is the electric field intensity at a point on the equatorial line of an electric dipole?
What is the electric field intensity at a point on the equatorial line of an electric dipole?
A charge q is uniformly distributed throughout a non-conducting sphere of radius $R$. What is the electric potential at the center of the sphere?
A charge q is uniformly distributed throughout a non-conducting sphere of radius $R$. What is the electric potential at the center of the sphere?
Two identical metal plates are given positive charges $Q_1$ and $Q_2$ where $Q_1 > Q_2$. The electric field intensity at a point between the plates is proportional to:
Two identical metal plates are given positive charges $Q_1$ and $Q_2$ where $Q_1 > Q_2$. The electric field intensity at a point between the plates is proportional to:
A parallel plate capacitor has a capacitance $C_0$ when there is vacuum between the plates. If a dielectric material with a dielectric constant K is inserted to completely fill the space between the plates, how does the capacitance change?
A parallel plate capacitor has a capacitance $C_0$ when there is vacuum between the plates. If a dielectric material with a dielectric constant K is inserted to completely fill the space between the plates, how does the capacitance change?
The energy stored in a capacitor is $U$. If the charge on the capacitor is doubled, what is the new energy stored?
The energy stored in a capacitor is $U$. If the charge on the capacitor is doubled, what is the new energy stored?
What is the electric flux through a closed surface enclosing an electric dipole?
What is the electric flux through a closed surface enclosing an electric dipole?
Flashcards
Coulomb's Law
Coulomb's Law
Force between two point charges
Electric Field Intensity
Electric Field Intensity
Force per unit charge
Electric Flux
Electric Flux
Measure of electric field through a surface
Gauss's Law
Gauss's Law
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Dipole Moment
Dipole Moment
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Linear Charge Density
Linear Charge Density
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Surface Charge Density
Surface Charge Density
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Volume Charge Density
Volume Charge Density
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Electric Potential
Electric Potential
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Capacitance
Capacitance
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Isolated Sphere Capacitance
Isolated Sphere Capacitance
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Electric Current
Electric Current
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Current Density
Current Density
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Drift Velocity
Drift Velocity
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Mobility
Mobility
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Resistivity
Resistivity
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EMF of Cell
EMF of Cell
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Terminal Potential Difference
Terminal Potential Difference
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Magnetic Field of Solenoid
Magnetic Field of Solenoid
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Bar Magnet as Solenoid
Bar Magnet as Solenoid
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Potential Energy of Dipole
Potential Energy of Dipole
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Permeability and Susceptibility
Permeability and Susceptibility
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Average AC Value
Average AC Value
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Inductive/Capacitive Reactance
Inductive/Capacitive Reactance
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Mirror Formula
Mirror Formula
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Refraction and Depth
Refraction and Depth
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Study Notes
Electric Charges & Fields
- Coulomb's Law calculates the electrostatic force, F, between two point charges, q1 and q2, separated by a distance, r
- The formula is F = k * |q1* q2| / r², where k = 1 / (4πε₀) ≈ 8.9875 × 10⁹ N⋅m²/C² is Coulomb's constant
- The formula varies slightly for vacuum and for different mediums, incorporating the permittivity of the medium
- Electric field intensity, E, is defined as the force per unit charge and is given by E = F / q
- Electric flux, Φ, for a uniform electric field is Φ = E ⋅ A = EAcosθ, while for non-uniform fields, it's the integral of E over the area
- Gauss's Law relates the electric flux through a closed surface to the net charge enclosed: ∮ E ⋅ dA = q_enclosed / ε₀
- Electric dipole moment is p = q * 2a, where q is the charge and 2a is the separation distance
- For a dipole placed in a uniform electric field, the torque τ = p × E and the net force is zero
- Electric field due to a dipole at an axial point is E = 2kP / r³, and at an equatorial point, E = kP / r³
- The electric field due to a uniformly charged sphere is E = kQ / r² for r ≥ R and E = 0 for r < R
Electric Potential & Capacitance
- Electric potential, V, is defined as V = q / (4πε₀r)
- The electric potential energy for two charges is U = q1*q2 / (4πε₀r)
- Relationship between electric field and potential: E = -dV/dr or V = -∫E ⋅ dr
- Capacitance, C, is defined as C = q / V
- For a parallel plate capacitor filled with air, C = ε₀A / d
- Capacitance of a spherical capacitor: C = 4πε₀ * (ab) / (b - a)
Current Electricity
- Electric current is the rate of flow of electric charge and is defined as i = dq/dt
- Current density, J, is the amount of current per unit area and is given by J = i / A
- Drift velocity, vd, is the average velocity of charge carriers and is given by vd = i / (neA), where n is the number density of charge carriers
- Ohm's Law states V = IR, where R is the resistance
- EMF of a cell E = V + Ir, where r is the internal resistance
- The principle of the Wheatstone bridge is P/Q = R/S
- Joule's Law describes the heat generated by a current: H = i²Rt
Moving Charges and Magnetism
- Magnetic force on a moving charge is given by F = q(v × B)
- The pitch of a helical path is p = 2πmvcosθ / (qB)
- Biot-Savart's Law helps calculate the magnetic field due to a current-carrying element: dB = (μ₀ / 4π) * (I dl × r) / r²
- Ampere's Circuital Law relates the integral of the magnetic field around a closed loop to the current passing through the loop
- The torque on a current-carrying coil in a uniform magnetic field is τ = NIABsinθ or τ = MBSinθ
- The magnetic field due to a current-carrying solenoid is B = μ₀nI = (μ₀NI)/l
Magnetism & Matter
- Potential energy of magnetic dipole is U = -MBcosθ or U = -M ⋅ B
- Curie's law relates magnetic susceptibility (χm) to temperature for paramagnetic materials
Electromagnetic Induction
- Magnetic flux Φ = B ⋅ A = BAcosθ
- Induced EMF is the negative rate of change of magnetic flux: E = -dΦ/dt
- Motional EMF is induced in a conductor moving through a magnetic field: E = BLv
- Self-inductance L = NΦ/I coefficient of self induction
- EMF induced in the could is e = -L di/dt
- Magnetic energy stored in an inductor: UB = (1/2)LI^2
Alternating Current
- Alternating current i = i₀sinωt
- Alternating voltage V = V₀sinωt
- RMS values are Irms = i₀/√2 and Vrms = V₀/√2
- Reactance XL = ωL and XC = 1/(ωC)
Ray Optics
- Mirror formula: 1/f=1/v+1/u is an equation that relates the focal length of a concave or convex lens to the distance of the object and the distance of the image
- Thin lens formula: 1/f=1/v-1/u is an equation that relates the focal length of a lens to the distance of the object and the distance of the image
- Lens maker's formula: 1=[n-1][1/R1 - 1/R2] is an equation that relates the focal length of a lens to the curvatures of its faces and the refractive index of its material
- Prism formula of small angle: S=(u-1)A with refraction at spherical surfaces
Wave Optics
- In interference of light Intensity of resultant wave I= I₁ + I₂ + 2√(I₁ I₂) cosФ
- Imax = (√I₁+ √I₂)² and Imin = (√I₁/√I₂)²
- For YDSE IP=4icos^2(Ф/2)
- In maxima PD = nλ
- In minima PD = (2n-1)λ/2
Dual Nature of Radiation and Matter
- Work function W = hν₀ = hc/λ₀
- Kmax = hν - Φ, where Φ is the work function
- Moving mass of photon m = E/c² = h/(λc)
- de Broglie wavelength λ = h/√2mK
Atoms
- Energy of electron Eₙ = -13.6 Z²/n² eV
- Bohr's radius rₙ = 0.53 n²/Z Å
- Velocity of electron v = 2.2 × 10⁶ Z/n m/s
Nuclei
- Nuclear radius R = R₀A¹/³, where R₀ ≈ 1.2 fm
- Mass defect Δm = [Zmp + (A-Z)mn] - mN
- Binding energy B.E. = Δmc²
Semiconductor Devices
- Total current through the pure semiconductor is I = Ie + Ih
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