SATHEE: electric-charges-and-fields Question 19

विद्युत आवेश और क्षेत्र

Question: Q. 9. A particle of mass $10^{- 3} kg$ and charge $5 μ C$ enters into a uniform electric field of $2 \times 10^{5} {NC}^{- 1}$ , moving with a velocity of $20 {ms}^{- 1}$ in a direction opposite to that of the field. Calculate the distance it would travel before coming to rest.

A [Delhi Comptt. I, II, III, 2012]

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Solution:

Ans. Here, $m = 10^{- 3} kg, q = 5 \times 10^{- 6} C, E = 2 \times 10^{5} N / C$ , $u = 20 m / s, v = 0$

As the particle enters opposite to the field, so it will retard.

Acceleration

$\begin{aligned} a & = - \frac{q E}{m} & = - \frac{5 \times 10^{- 6} \times 2 \times 10^{5}}{10^{- 3}} \end{aligned}$

$= - 10^{3} m / s^{2}$

Using,

$v^{2} = u^{2} - 2 a s$

$0 = (20)^{2} - 2 \times 1000 \times s$

$\Rightarrow s = \frac{400}{2000} = \frac{1}{5} = 0.2 m$

[CBSE Marking Scheme, 2012]

Unstable equilibrium $θ = 180^{\circ}$

[CBSE Marking Scheme, 2017]

(AI) Q. 2. (i) Obtain the expression for the torque $\vec{τ}$ experienced by an electric dipole of dipole moment $\vec{p}$ in a uniform electric field, $\vec{E}$ .

(ii) What will happen if the field were not uniform?

R [Delhi III 2017]

Ans. (i) Obtaining expression for torque $\vec{τ}$ experienced by electric dipole in uniform electric field 2

(ii) Effect of non-uniform electric field

(i) Force on $+ q, \vec{F} = q \vec{E}$

Force on $- q, \vec{F} = - q \vec{E}$

Magnitude of torque $\vec{τ} = q E \times 2 a \sin θ$

$= 2 q a E \sin θ$

$\vec{τ} = \vec{p} \times \vec{E}$

(ii) If the electric field is non-uniform, the dipole experiences a translatory force as well as a torque.

[CBSE Marking Scheme, 2017]

Detailed Answer :

(i)

Consider electric dipole kept in an uniform electric field at an angle $θ$ where a dipole experience a torque, so, torque generated by parallel forces $q E$ will act as couple as

$\begin{aligned} | \vec{τ} | & = q E 2 l \sin θ & = p E \sin θ [as p = 2 q l] 1 / 2 | \vec{τ} | & = | \vec{p} \times \vec{E} | \end{aligned}$

(ii) When the field is non-uniform, force acting on both ends will not be equal, hence they result in mixture of couple and net force. With this, dipole experiences rotational as well as linear force. $1$

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Detailed Answer :

विषयसूची

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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