NEET Electric Charges and Fields — Set 7

Question 1

Two charges $ +12 \, \mu\text{C} $ and $ -4 \, \mu\text{C} $ are 90 cm apart. What is the distance from $ +12 \, \mu\text{C} $ where the electric field is zero?

Accepted Answer

Let $ x $ be distance from $ +12 \, \mu\text{C} $, then $ 0.9 - x $ from $ -4 \, \mu\text{C} $. $ \frac{12 \times 10^{-6}}{x^2} = \frac{4 \times 10^{-6}}{(0.9 - x)^2} $, $ 12 (0.9 - x)^2 = 4 x^2 $. $ 3 (0.81 - 1.8 x + x^2) = x^2 $, $ 2.43 - 5.4 x + 3 x^2 = x^2 $. $ 2 x^2 - 5.4 x + 2.43 = 0 $, $ x = \frac{5.4 \pm \sqrt{29.16 - 19.44}}{4} = \frac{5.4 \pm 3.12}{4} $. $ x = 0.57 \, \text{m} $ (between charges).

Question 2

A dipole with $ p = 5 \times 10^{-9} \, \text{C m} $ is at 90° to a field $ E = 5 \times 10^4 \, \text{N/C} $. What is the torque?

Accepted Answer

$ \tau = p E \sin \theta $. $ \tau = 5 \times 10^{-9} \times 5 \times 10^4 \times \sin 90^\circ = 25 \times 10^{-5} \times 1 = 2.5 \times 10^{-4} \, \text{N m} $.

Question 3

An infinite line charge has $ \lambda = 8 \times 10^{-7} \, \text{C/m} $. What is the electric field at 20 cm?

Accepted Answer

$ E = \frac{2 k \lambda}{r} $, $ k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 $. $ E = \frac{2 \times 9 \times 10^9 \times 8 \times 10^{-7}}{0.2} = 7.2 \times 10^4 \, \text{N/C} $.

NEET Physics: Electric Charges and Fields — Practice Set 7

Q1. Two charges \( +12 \, \mu\text{C} \) and \( -4 \, \mu\text{C} \) are 90 cm apart. What is the distance from \( +12 \, \mu\text{C} \) where the electric field is zero?

Q2. A dipole with \( p = 5 \times 10^{-9} \, \text{C m} \) is at 90° to a field \( E = 5 \times 10^4 \, \text{N/C} \). What is the torque?

Q3. An infinite line charge has \( \lambda = 8 \times 10^{-7} \, \text{C/m} \). What is the electric field at 20 cm?

Q4. Two charges \( +14 \, \mu\text{C} \) and \( -6 \, \mu\text{C} \) are 100 cm apart. What is the distance from \( +14 \, \mu\text{C} \) where the electric field is zero?

Q5. Why does the electric field due to a uniformly charged wire drop off more slowly with distance compared to a point charge?

Q6. Which principle explains why rubbing two neutral objects can result in one becoming positively charged and the other negatively charged?

Q7. What allows the electric field to be discontinuous across a charged surface, such as a conductor’s boundary?

Q8. A thin spherical shell of radius 20 cm has a charge of \( 14 \, \mu\text{C} \). What is the electric field at a point 25 cm from the center?

Q9. A conducting sphere of radius 10 cm has a surface charge density of \( 20 \, \mu\text{C/m}^2 \). What is the electric field just outside its surface?

Q10. Two charges \( +3 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are 15 cm apart. What is the force on a \( 2 \, \mu\text{C} \) charge placed at the midpoint?

Q11. Three charges \( +q, +q, -q \) are at the vertices of an equilateral triangle of side 3 m. What is the net force magnitude on \( +q \) at one vertex?

Q12. A charge of \( 8 \, \mu\text{C} \) is at the center of a cube of edge 25 cm. What is the total flux through the cube?

Q13. A charge of \( 4 \, \mu\text{C} \) is placed at the center of a cube of edge 10 cm. What is the electric flux through one face?

Q14. A uniform field \( E = 9 \times 10^3 \, \text{N/C} \) is along the x-axis. What is the flux through a rectangle of 15 cm × 20 cm in the yz-plane?

Q15. A dipole with \( p = 7 \times 10^{-9} \, \text{C m} \) is at 45° to a field \( E = 9 \times 10^4 \, \text{N/C} \). What is the torque?