NEET Electric Charges and Fields — Set 14

Question 1

Three charges $ +4 \, \mu\text{C}, -4 \, \mu\text{C}, +2 \, \mu\text{C} $ are at the vertices of an equilateral triangle of side 1 m. What is the force magnitude on $ +4 \, \mu\text{C} $?

Accepted Answer

$ F_1 = 9 \times 10^9 \times \frac{4 \times 4 \times 10^{-12}}{1} = 0.144 \, \text{N} $ (attractive). $ F_2 = 9 \times 10^9 \times \frac{4 \times 2 \times 10^{-12}}{1} = 0.072 \, \text{N} $ (repulsive). Angle 60°. Net $ F = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos 60^\circ} = \sqrt{0.144^2 + 0.072^2 + 0.010368} = 0.187 \, \text{N} $.

Question 2

An infinite line charge produces an electric field of $ 1.8 \times 10^5 \, \text{N/C} $ at 3 cm. What is its linear charge density?

Accepted Answer

$ E = \frac{\lambda}{2 \pi \varepsilon_0 r} $, or $ E = \frac{2 k \lambda}{r} $, $ k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 $. $ 1.8 \times 10^5 = \frac{2 \times 9 \times 10^9 \times \lambda}{0.03} $. $ \lambda = \frac{1.8 \times 10^5 \times 0.03}{18 \times 10^9} = 3 \times 10^{-7} \, \text{C/m} $.

Question 3

A conducting sphere of radius 18 cm has a surface charge density of $ 25 \, \mu\text{C/m}^2 $. What is the electric field just outside its surface?

Accepted Answer

For a conductor: $ E = \frac{\sigma}{\varepsilon_0} $. $ E = \frac{25 \times 10^{-6}}{8.854 \times 10^{-12}} = 2.82 \times 10^6 \, \text{N/C} $.

NEET Physics: Electric Charges and Fields — Practice Set 14

Q1. Three charges \( +4 \, \mu\text{C}, -4 \, \mu\text{C}, +2 \, \mu\text{C} \) are at the vertices of an equilateral triangle of side 1 m. What is the force magnitude on \( +4 \, \mu\text{C} \)?

Q2. An infinite line charge produces an electric field of \( 1.8 \times 10^5 \, \text{N/C} \) at 3 cm. What is its linear charge density?

Q3. A conducting sphere of radius 18 cm has a surface charge density of \( 25 \, \mu\text{C/m}^2 \). What is the electric field just outside its surface?

Q4. Why does the electric field due to a charged conducting sphere remain constant just outside its surface regardless of its radius?

Q5. What ensures that the electric field lines from a positive point charge always point radially outward?

Q6. Why does the electric field due to a dipole exhibit a stronger angular dependence compared to a single point charge?

Q7. A uniform electric field \( E = 2 \times 10^4 \, \text{N/C} \) is along the x-axis. What is the flux through a square of side 20 cm in the yz-plane?

Q8. A body acquires a charge of \( -9.6 \times 10^{-8} \, \text{C} \) when rubbed. How many electrons were transferred to it?

Q9. A conducting sphere of radius 15 cm has an electric field of \( 4 \times 10^3 \, \text{N/C} \) at 30 cm from its center. What is the charge?

Q10. A uniform field \( E = 5 \times 10^3 \, \text{N/C} \) is along the x-axis. What is the flux through a circle of radius 20 cm in the yz-plane?