NEET Electric Charges and Fields — Set 10

Question 1

A conducting sphere of radius 27 cm has an electric field of $ 6 \times 10^3 \, \text{N/C} $ at 54 cm from its center. What is the charge?

Accepted Answer

$ E = \frac{k q}{r^2} $. $ 6 \times 10^3 = 9 \times 10^9 \times \frac{q}{(0.54)^2} $. $ q = \frac{6 \times 10^3 \times 0.2916}{9 \times 10^9} = 1.944 \times 10^{-7} \, \text{C} $.

Question 2

Two charges $ +12 \, \mu\text{C} $ and $ -3 \, \mu\text{C} $ are 60 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 $ 0.6 - x $ from $ -3 \, \mu\text{C} $. $ \frac{12 \times 10^{-6}}{x^2} = \frac{3 \times 10^{-6}}{(0.6 - x)^2} $, $ 12 (0.6 - x)^2 = 3 x^2 $. $ 4 (0.36 - 1.2 x + x^2) = x^2 $, $ 1.44 - 4.8 x + 4 x^2 = x^2 $. $ 3 x^2 - 4.8 x + 1.44 = 0 $, $ x = \frac{4.8 \pm \sqrt{23.04 - 17.28}}{6} = \frac{4.8 \pm 2.4}{6} $. $ x = 0.4 \, \text{m} $ (between charges).

Question 3

An infinite line charge has $ E = 6.3 \times 10^5 \, \text{N/C} $ at 7 cm. What is $ \lambda $?

Accepted Answer

$ E = \frac{2 k \lambda}{r} $. $ 6.3 \times 10^5 = \frac{2 \times 9 \times 10^9 \times \lambda}{0.07} $. $ \lambda = \frac{6.3 \times 10^5 \times 0.07}{18 \times 10^9} = 2.45 \times 10^{-6} \, \text{C/m} $.

NEET Physics: Electric Charges and Fields — Practice Set 10

Q1. A conducting sphere of radius 27 cm has an electric field of \( 6 \times 10^3 \, \text{N/C} \) at 54 cm from its center. What is the charge?

Q2. Two charges \( +12 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are 60 cm apart. What is the distance from \( +12 \, \mu\text{C} \) where the electric field is zero?

Q3. An infinite line charge has \( E = 6.3 \times 10^5 \, \text{N/C} \) at 7 cm. What is \( \lambda \)?

Q4. A point charge \( 10 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 5 m along the z-axis?

Q5. A glass rod is rubbed with silk and acquires a charge of \( +2.5 \times 10^{-7} \, \text{C} \). How many electrons were transferred from the glass rod to the silk?

Q6. A plastic rod gains \( 4.8 \times 10^{-8} \, \text{C} \) of negative charge when rubbed. How many electrons were transferred to it?

Q7. An infinite line charge has \( \lambda = 1.2 \times 10^{-6} \, \text{C/m} \). What is the electric field at 40 cm?

Q8. Two charges \( +10 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) are 80 cm apart. What is the distance from \( +10 \, \mu\text{C} \) where the electric field is zero?

Q9. A point charge \( -9 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 6 m along the x-axis?

Q10. A uniform field \( E = 6 \times 10^3 \, \text{N/C} \) is along the y-axis. What is the flux through a rectangle of 40 cm × 25 cm in the xz-plane at 45° to the y-axis?