SATHEE: Electrostatics 7 Question 17

Electrostatics 7 Question 17

17. The average current in the steady state registered by the ammeter in the circuit will be

(2016 Adv.)

(a) proportional to $V_{0}^{2}$ .

(b) proportional to the potential $V_{0}$ .

(d) proportions to $V_{0}^{1 / 2}$

Match the Column

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Solution:

As the balls keep on carrying charge form one plate to another, current will keep on flowing even in steady state. When at bottom plate, if all balls attain charge $q$ ,

$\begin{aligned} \frac{k q}{r} & = V_{0} & ∴ k = \frac{1}{4 π ε_{0}} \\ \Rightarrow & q & = \frac{V_{0} r}{k} \end{aligned}$

Inside cylinder, electric field $E = [V_{0} - (- V_{0})] h$

$= 2 V_{0} h$

$\Rightarrow$ Acceleration of each ball,

$a = \frac{q E}{m} = \frac{2 h r}{k m} \cdot V_{0}^{2}$

$\Rightarrow$ Time taken by balls to reach other plate,

$t = \sqrt{\frac{2 h}{a}} = \sqrt{\frac{2 h \cdot k m}{2 h r V_{0}^{2}}} = \frac{1}{V_{0}} \sqrt{\frac{k m}{r}}$

If there are $n$ balls, then

Average current, $i_{a v} = \frac{n q}{t} = n \times \frac{V_{0} r}{k} \times V_{0} \sqrt{\frac{r}{k m}}$

$\Rightarrow i_{a v} \propto V_{0}^{2}$

18. List-II

(1) $E = \frac{1}{4 π ε_{0}} \frac{Q}{d^{2}}$

$\Rightarrow E \propto \frac{1}{d^{2}}$

(2) $E_{axis} = \frac{1}{4 π ε_{0}} \frac{2 Q (2 l)}{d^{3}}$

$\Rightarrow E \propto \frac{1}{d^{3}}$

(3) $E = \frac{λ}{2 π ε_{0} d} \Rightarrow E \propto \frac{1}{d}$

(4) $E = \frac{λ}{2 π ε_{0} (d - l)} - \frac{λ}{2 π ε_{0} (d + l)} = \frac{λ (2 l)}{2 π ε_{0} d^{2}}$

$\Rightarrow E \propto \frac{1}{d^{2}}$

(5) $E = \frac{σ}{2 ε_{0}} \Rightarrow$ E is independent of $d$

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Electrostatics 7 Question 17

17. The average current in the steady state registered by the ammeter in the circuit will be

Match the Column

Solution:

18. List-II

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Electrostatics 7 Question 17

17. The average current in the steady state registered by the ammeter in the circuit will be

Match the Column

Solution:

18. List-II

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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