[Case Study, Q29 contd.] (iv)(a) Let $E_1,E_2,E_3,E_4$ be the magni...

Question

[Case Study, Q29 contd.] (iv)(a) Let $E_1,E_2,E_3,E_4$ be the magnitudes of the electric field between the pairs of plates I, II, III, IV respectively. Compare them.

OR (b) An electron is projected from the right plate of Set I directly towards its left plate. It just comes to rest at the plate. Find the speed with which it was projected. (Take $e/m=1.76\times10^{11}$ C/kg)

Accepted Answer

Part (a): Step 1: $E = \Delta V/d$ (d is same = 2cm for all sets), so compare $|\Delta V|$ for each: Set I: $|-50-(-70)|=20$V. Set II: $|150-(-50)|=200$V. Set III: $|200-(-20)|=220$V. Set IV: $|-400-(-100)|=300$V.

Step 2: So $E_4>E_3>E_2>E_1$ (using same d for all). Comparing with options, this matches: (C) $E_4>E_3>E_2>E_1$.

Part (b) OR: Step 1: By work-energy theorem, KE lost = work done against the field = $e\Delta V$, where $\Delta V=20$V (Set I).

Step 2: $\frac12mv^2 = e\Delta V \Rightarrow v = \sqrt{2(e/m)\Delta V} = \sqrt{2\times1.76\times10^{11}\times20}$.

Step 3: $v = \sqrt{7.04\times10^{12}} \approx 2.65\times10^6$ m/s.

Step 4: Answer: (B) $2.6\times10^6$ m/s.

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