NEET Electric Charges and Fields — Set 16

Question 1

A dipole with charges $ +6 \, \mu\text{C} $ and $ -6 \, \mu\text{C} $ separated by 4 mm is in a field $ 5 \times 10^4 \, \text{N/C} $ at 60°. What is the torque?

Accepted Answer

Dipole moment: $ p = q \times 2a = 6 \times 10^{-6} \times 4 \times 10^{-3} = 2.4 \times 10^{-8} \, \text{C m} $. Torque: $ \tau = p E \sin \theta = 2.4 \times 10^{-8} \times 5 \times 10^4 \times \sin 60^\circ = 1.2 \times 10^{-3} \times \frac{\sqrt{3}}{2} = 1.04 \times 10^{-3} \, \text{N m} $.

Question 2

An infinite line charge has $ \lambda = 5 \times 10^{-7} \, \text{C/m} $. What is the electric field at 10 cm?

Accepted Answer

$ E = \frac{2 k \lambda}{r} $. $ E = \frac{2 \times 9 \times 10^9 \times 5 \times 10^{-7}}{0.1} = 9 \times 10^4 \, \text{N/C} $.

Question 3

Two charges $ +6 \, \mu\text{C} $ and $ -4 \, \mu\text{C} $ are 25 cm apart. What is the distance from $ +6 \, \mu\text{C} $ where the electric field is zero?

Accepted Answer

Let distance from $ +6 \, \mu\text{C} $ be $ x $, then from $ -4 \, \mu\text{C} $ is $ 0.25 - x $. $ \frac{k \times 6 \times 10^{-6}}{x^2} = \frac{k \times 4 \times 10^{-6}}{(0.25 - x)^2} $. $ \frac{6}{x^2} = \frac{4}{(0.25 - x)^2} $, $ 6 (0.25 - x)^2 = 4 x^2 $. $ 6 (0.0625 - 0.5 x + x^2) = 4 x^2 $, $ 0.375 - 3 x + 6 x^2 = 4 x^2 $. $ 2 x^2 - 3 x + 0.375 = 0 $, $ x = \frac{3 \pm \sqrt{9 - 3}}{4} = \frac{3 \pm \sqrt{6}}{4} $. $ x = 0.15 \, \text{m} $ (between charges).

NEET Physics: Electric Charges and Fields — Practice Set 16

Q1. A dipole with charges \( +6 \, \mu\text{C} \) and \( -6 \, \mu\text{C} \) separated by 4 mm is in a field \( 5 \times 10^4 \, \text{N/C} \) at 60°. What is the torque?

Q2. An infinite line charge has \( \lambda = 5 \times 10^{-7} \, \text{C/m} \). What is the electric field at 10 cm?

Q3. Two charges \( +6 \, \mu\text{C} \) and \( -4 \, \mu\text{C} \) are 25 cm apart. What is the distance from \( +6 \, \mu\text{C} \) where the electric field is zero?

Q4. A uniform electric field \( E = 4 \times 10^3 \, \text{N/C} \) is along the x-axis. What is the flux through a square of side 70 cm in the yz-plane?

Q5. Which property of electric field lines ensures they never intersect, even in complex charge distributions?

Q6. What causes the electric field to be discontinuous across a charged surface, such as a thin sheet?

Q7. A thin spherical shell of radius 19 cm has \( q = 7 \, \mu\text{C} \). What is the electric field at 15 cm from the center?

Q8. A dipole with charges \( +6 \, \mu\text{C} \) and \( -6 \, \mu\text{C} \) separated by 2 mm is in a field \( 8 \times 10^4 \, \text{N/C} \) at 60°. What is the torque?

Q9. A uniform electric field \( E = 6 \times 10^3 \, \text{N/C} \) is along the z-axis. What is the flux through a square of side 50 cm in the xy-plane?

Q10. A dipole with \( p = 8 \times 10^{-9} \, \text{C m} \) is at 90° to a field \( E = 6 \times 10^4 \, \text{N/C} \). What is the torque?