NEET Electric Charges and Fields — Set 12

Question 1

Why does the electric field inside a charged conducting shell remain unaffected by charges placed outside it?

Accepted Answer

Gauss’s law shows that the field inside depends only on enclosed charge. External charges induce surface charges on the conductor, but these adjust to cancel the external field inside, leaving it zero regardless of outside charges.

Question 2

Three charges $ +5 \, \mu\text{C}, -3 \, \mu\text{C}, +4 \, \mu\text{C} $ are at the vertices of an equilateral triangle of side 1.5 m. What is the force magnitude on $ +5 \, \mu\text{C} $?

Accepted Answer

$ F_1 = 9 \times 10^9 \times \frac{5 \times 3 \times 10^{-12}}{(1.5)^2} = 0.06 \, \text{N} $ (attractive). $ F_2 = 9 \times 10^9 \times \frac{5 \times 4 \times 10^{-12}}{(1.5)^2} = 0.08 \, \text{N} $ (repulsive). Angle 60°. Net $ F = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos 60^\circ} = \sqrt{0.06^2 + 0.08^2 + 0.0048} = 0.108 \, \text{N} $.

Question 3

A conducting sphere of radius 29 cm has a surface charge density of $ 50 \, \mu\text{C/m}^2 $. What is the total charge?

Accepted Answer

Surface area: $ A = 4 \pi r^2 = 4 \pi (0.29)^2 = 0.335 \pi \, \text{m}^2 $. Charge: $ q = \sigma A = 50 \times 10^{-6} \times 0.335 \pi = 5.27 \times 10^{-5} \, \text{C} $.

NEET Physics: Electric Charges and Fields — Practice Set 12

Q1. Why does the electric field inside a charged conducting shell remain unaffected by charges placed outside it?

Q2. Three charges \( +5 \, \mu\text{C}, -3 \, \mu\text{C}, +4 \, \mu\text{C} \) are at the vertices of an equilateral triangle of side 1.5 m. What is the force magnitude on \( +5 \, \mu\text{C} \)?

Q3. A conducting sphere of radius 29 cm has a surface charge density of \( 50 \, \mu\text{C/m}^2 \). What is the total charge?

Q4. A dipole with charges \( +3 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) separated by 5 mm is in a field \( 8 \times 10^4 \, \text{N/C} \) at 45°. What is the torque?

Q5. A dipole with charges \( +5 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) separated by 3 mm is in a field of \( 2 \times 10^4 \, \text{N/C} \) at 45°. What is the torque?

Q6. Two charges \( +11 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) are 80 cm apart. What is the electric field magnitude at the midpoint?

Q7. Two charges \( +8 \, \mu\text{C} \) and \( -4 \, \mu\text{C} \) are 40 cm apart. What is the electric field magnitude at the midpoint?

Q8. A thin spherical shell of radius 24 cm has a charge of \( 16 \, \mu\text{C} \). What is the electric field at a point 30 cm from the center?

Q9. What property of insulators causes charges to remain localized when applied to their surface?

Q10. Three charges \( +5 \, \mu\text{C}, -5 \, \mu\text{C}, +2 \, \mu\text{C} \) are at the vertices of an equilateral triangle of side 1.5 m. What is the force magnitude on \( +5 \, \mu\text{C} \)?