A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of 25.5 kVm -1. The density of liquid is 1.26 × 10³ kg m -3. The radius of the drop is (neglect buoyancy). (a) 4.3 × 10⁻⁷ m (b) 7.8 × 10⁻⁷ m (c) 0.078 × 10⁻⁷ m (d) 3.4 × 10⁻⁷ m

Answer: (b). Balance: 6eE = ρ4/3π r³ g r³ = 6 × 1.6 × 10⁻¹⁹ × 25.5 × 10³1.26 × 10³ × 4/3π × 9.8 = 2.45 × 10⁻¹⁴5.17 × 10⁴ ≈ 4.73 × 10⁻¹⁹ m³ r ≈ 7.8 × 10⁻⁷ m So the answer is (b) 7.8 × 10⁻⁷ m.

A liquid drop having 6 excess electrons is kept stationary under a… | JEE Main 2013 (23 Apr, Shift 1)

Q40JEE Main 2013 · 23 APR · SHIFT 1Medium

Motion of Charges in an Electric Field

A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of 25.5 kVm $-1$ . The density of liquid is $1.26 \times 10^{3}$ kg m $-3$ . The radius of the drop is (neglect buoyancy).

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Answer: (b)

Balance: $6eE = \rho\frac{4}{3}\pi r^3 g$
$r^3 = \frac{6 \times 1.6 \times 10^{-19} \times 25.5 \times 10^{3}}{1.26 \times 10^{3} \times \frac{4}{3}\pi \times 9.8} = \frac{2.45 \times 10^{-14}}{5.17 \times 10^{4}} \approx 4.73 \times 10^{-19}\text{ m}^3$
$r \approx 7.8 \times 10^{-7}\text{ m}$
So the answer is (b) $7.8 \times 10^{-7}\text{ m}$ .

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