WBJEE Physics - Electromagnetism, Optics and Modern Physics Flashcards

24 sample cards from the Physics - Electromagnetism, Optics and Modern Physics deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. On what does the speed of sound in a gas depend, per Laplace's formula?

   $v = \sqrt{\dfrac{\gamma P}{\rho}}$, where $\gamma$ is the adiabatic ratio $C_p/C_v$, $P$ is pressure, and $\rho$ is density. Speed increases with temperature: $v \propto \sqrt{T}$.

2. How is sound intensity related to amplitude and to distance from a point source?

   Intensity $I \propto A^{2}$ (proportional to amplitude squared) and $I \propto \dfrac{1}{r^{2}}$ (inverse-square law from a point source).

3. State the general Doppler effect formula for the observed frequency of sound.

   $f' = f\left(\dfrac{v \pm v_o}{v \mp v_s}\right)$, where $v$ is sound speed, $v_o$ observer speed, $v_s$ source speed; signs are chosen so relative approach increases $f'$.

4. Using the Doppler formula, what is the observed frequency when the source moves toward a stationary observer?

   $f' = f\left(\dfrac{v}{v - v_s}\right)$, which is greater than $f$ (perceived pitch rises as the source approaches).

5. State Coulomb's law in vector form.

   $\vec{F} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r^{2}}\hat{r}$, the force between two point charges; it is attractive for unlike and repulsive for like charges. $\dfrac{1}{4\pi\varepsilon_0} \approx 9\times10^{9}\,\text{N m}^2/\text{C}^2$.

6. Define the electric field and give its value due to a point charge.

   Electric field is force per unit positive test charge: $\vec{E} = \dfrac{\vec{F}}{q_0}$. For a point charge: $E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^{2}}$.

7. State Gauss's law.

   The net electric flux through a closed surface equals the enclosed charge divided by $\varepsilon_0$: $\oint \vec{E}\cdot d\vec{A} = \dfrac{q_{enc}}{\varepsilon_0}$.

8. Use Gauss's law to give the electric field of an infinite line charge with linear density $\lambda$.

   $E = \dfrac{\lambda}{2\pi\varepsilon_0 r}$, directed radially; it falls off as $\dfrac{1}{r}$.

9. What is the electric field due to an infinite charged plane sheet with surface density $\sigma$?

   $E = \dfrac{\sigma}{2\varepsilon_0}$, uniform and independent of distance from the sheet.

10. What is the electric field inside and outside a uniformly charged conducting spherical shell of charge $Q$ and radius $R$?

    Inside ($r<R$): $E = 0$. Outside ($r>R$): $E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{r^{2}}$, as if all charge were at the center.

11. Define electric potential and give its value due to a point charge.

    Electric potential is work done per unit charge to bring a positive test charge from infinity to a point: $V = \dfrac{W}{q_0}$. For a point charge: $V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r}$.

12. What is the relation between electric field and potential?

    $\vec{E} = -\nabla V$; in one dimension $E_x = -\dfrac{dV}{dx}$. The field points toward decreasing potential.

13. Give the electric potential energy of a system of two point charges.

    $U = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r}$. It is positive for like charges and negative for unlike charges.

14. Define capacitance and give the capacitance of a parallel-plate capacitor.

    Capacitance $C = \dfrac{Q}{V}$ (charge stored per unit potential). For a parallel-plate capacitor: $C = \dfrac{\varepsilon_0 A}{d}$, where $A$ is plate area and $d$ the separation.

15. How does inserting a dielectric of constant $K$ affect a capacitor's capacitance?

    Capacitance increases by factor $K$: $C = \dfrac{K\varepsilon_0 A}{d}$. The dielectric reduces the internal field by factor $K$ and allows more charge storage.

16. Give the equivalent capacitance for capacitors in series and in parallel.

    Series: $\dfrac{1}{C_{eq}} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dots$ (smaller). Parallel: $C_{eq} = C_1 + C_2 + \dots$ (larger).

17. Give three expressions for the energy stored in a capacitor.

    $U = \dfrac{1}{2}CV^{2} = \dfrac{1}{2}QV = \dfrac{Q^{2}}{2C}$.

18. State Ohm's law and define resistance.

    Ohm's law: $V = IR$, the current through a conductor is proportional to the potential difference (at constant temperature). Resistance $R = \dfrac{V}{I}$, measured in ohms ($\Omega$).

19. How does the resistance of a wire depend on its dimensions and resistivity?

    $R = \rho\dfrac{L}{A}$, where $\rho$ is resistivity, $L$ is length, and $A$ is cross-sectional area. $R$ increases with length and decreases with area.

20. Give the formulas for equivalent resistance in series and in parallel.

    Series: $R_{eq} = R_1 + R_2 + \dots$ Parallel: $\dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots$

21. Express current in terms of drift velocity of electrons.

    $I = nAev_d$, where $n$ is number density of free electrons, $A$ cross-sectional area, $e$ electron charge, and $v_d$ the drift velocity.

22. How does the resistivity of a metallic conductor vary with temperature?

    It increases approximately linearly: $\rho_T = \rho_0[1 + \alpha(T - T_0)]$, where $\alpha$ is the temperature coefficient of resistivity (positive for metals).

23. State the relation between terminal voltage, EMF, and internal resistance of a cell.

    $V = \varepsilon - Ir$, where $\varepsilon$ is the EMF, $I$ the current, and $r$ the internal resistance. The current delivered is $I = \dfrac{\varepsilon}{R + r}$.

24. Give the formulas for electric power dissipated in a resistor.

    $P = VI = I^{2}R = \dfrac{V^{2}}{R}$. Energy dissipated as heat over time $t$ is $H = I^{2}Rt$ (Joule heating).

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