Download App

Electric Field and Potential — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsElectric Field and Potential5 Marks
Question
Two particles A and B, each carrying a charge Q, are held fixed with a separation d between them. A particle C having mass m and charge q is kept at the middle point of the line AB.
  1. If it is displaced through a distance x perpendicular to AB, what would be the electric force experienced by it.
  2. Assuming x << d, show that this force is proportional to x.
  3. Under what conditions will the particle C execute simple harmonic motion if it is released after such a small displacement?
Find the time period of the oscillations if these conditions are satisfied.
✓

Answer


  1. Let Q = charge on A & B Separated by distance d

q = charge on c displaced $\bot$ to -AB

So, force on $0=\overline{\text{F}}_\text{AB}+\overline{\text{F}}_\text{BO}$

But $\text{F}_\text{AO}\cos\theta=\text{F}_\text{BO}\cos\theta$

So, force on ‘0’ in due to vertical component.

$\overline{\text{F}}=\text{F}_\text{AO}\sin\theta+\text{F}_\text{BO}\sin\theta$ $|\text{F}_\text{AO}|=|\text{F}_\text{BO}|$

$=2\frac{\text{KQq}}{\Big(\frac{\text{d}}{2^2+\text{x}^2}\big)}\sin\theta$

$\text{F}=\frac{2\text{KQq}}{\Big(\frac{\text{d}}{2}\Big)^2+\text{x}^2}\sin\theta$

$=\frac{4\times2\times2\text{KQq}}{(\text{d}^2+4\text{x}^2)}\times\frac{\text{x}}{\Big[\big(\frac{\text{d}}{2}\big)^2+\text{x}^2\Big]^{\frac{1}{2}}}$

$=\frac{2\text{kQq}}{\Big[\big(\frac{\text{d}}{2}\big)^2+\text{x}^2\Big]^{\frac{3}{2}}}\text{x}$ = Electric force $\Rightarrow\text{F}\propto\text{x}$

  1. When x << d

$\text{F}=\frac{2\text{kQq}}{\Big[\big(\frac{\text{d}}{2}\big)^2+\text{x}^2\Big]^{\frac{3}{2}}}\text{x}$ x << d

$\Rightarrow\text{F}=\frac{2\text{kQq}}{\Big(\frac{\text{d}^2}{4}\Big)^{\frac{3}{2}}}\text{x}\Rightarrow\text{F}\propto\text{x}$

$\text{a}=\frac{\text{F}}{\text{m}}=\frac{1}{\text{m}}\Bigg[\frac{2\text{kQqx}}{\Big[\big(\frac{\text{d}^2}{4}\big)+\ell^2}\Bigg]$

So time period $\text{T}=2\pi\sqrt{\frac{\ell}{\text{g}}}$

$=2\pi\sqrt{\frac{\ell}{\text{a}}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Long Answer Type Questions [5M]" from Electric Field and Potential→Electric Field and Potential — all question types→Physics STD 12 Science question papers→Bihar Board STD 12 Science question papers→Bihar Board question paper generator→

Similar questions

A pendulum clock gives correct time at 20°C at a place where g = 9.800m s-2. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g = 9.788m s-2. At what temperature will it give correct time ? Coefficient of linear expansion of steel = 12 × 10-6 °C-1.
→
A chain of length l and mass m lies on the surface of a smooth sphere of radius R>1 with one end tied to the top of the sphere.
  1. Find the gravitational potential energy of the chain with reference level at the centre of the sphere.
  2. Suppose the chain is released and slides down the sphere. Find the kinetic energy of the chain, when it has slid through an angle $\theta.$
  3. Find the tangential acceleration $\frac{\text{dv}}{\text{dt}}$ of the chain when the chain starts sliding down.
→
Derive an expression for the electric potential at a point due to an electric dipole. Mention the contrasting features of electric potential of a dipole at a point as compared to that due to a single charge.
→
The temperature and pressure at Simla are 15.0°C and 72.0cm of mercury and at Kalka these are 35.0°C and 76.0cm of mercury. Find the ratio of air density at Kalka to the air density at Simla.
→
What is the
  1. Momentum,
  2. Speed, and
  3. De Broglie wavelength of an electron with kinetic energy of 120 eV.
→
A circuit containing a 80 mH inductor and a $60 \mu F$ capacitor in series is connected to a $230 V, 50 Hz$ supply. The resistance of the circuit is negligible.
a. Obtain the current amplitude and rms values.
b. Obtain the rms values of potential drops across each element.
c. What is the average power transferred to the inductor?
d. What is the average power transferred to the capacitor?
e. What is the total average power absorbed by the circuit? [‘Average’ implies ‘averaged over one cycle’.]
→
Establish the formula for the capacitance of a parallel plate capacitor in the presence of dielectric material completely and partially.
→
The current−voltage characteristic of an ideal p-n junction diode is given by $\text{i}=\text{i}_0\Big(\text{e}^{\frac{\text{eV}}{\text{kT}}}-1\Big)$ where, the drift current i0 equals $10\mu\text{A}.$ Take the temperature T to be 300K.
  1. Find the voltage V0 for which $\text{e}^{\frac{\text{eV}}{\text{KT}}}=100.$ One can neglect the term 1 for voltages greater than this value.
  2. Find an expression for the dynamic resistance of the diode as a function of V for V > V0.
  3. Find the voltage for which the dynamic resistance is $0.2\Omega.$
→
Figure shows a potentiometer with a cell of 2.0V and internal resistance of $0.40\Omega$ maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02V (for very moderate currents upto a few mA) gives a balance point at 67.3cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of $600\text{k}\Omega$ is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf and the balance point found similarly, turns out to be at 82.3cm length of the wire.

  1. What is the value of $\varepsilon?$
  2. What purpose does the high resistance of $600\text{k}\Omega$ have?
  3. Is the balance point affected by this high resistance?
  4. Is the balance point affected by the internal resistance of the driver cell?
  5. Would the method work in the above situation if the driver cell of the potentiometer had an emf of 1.0V instead of 2.0V?
  6. Would the circuit work well for determining extremely small emf, say of the order of few mV (such as the typical emf of a thermo couple)? If not, how would you modify the circuit?
→
A particle of mass m and charge q is released from the origin in a region in which the electric field and magnetic field are given by
$\overrightarrow{\text{B}}=-\text{B}_0\overrightarrow{\text{j}}$ and $\overrightarrow{\text{E}}=\text{E}_0\overrightarrow{\text{k}}.$ Find the speed of the particle as a function of its z-coordinate.
→