NEET Electric Charges and Fields — Set 20

Question 1

Two charges $ +15 \, \mu\text{C} $ and $ -5 \, \mu\text{C} $ are 75 cm apart. What is the distance from $ +15 \, \mu\text{C} $ where the electric field is zero?

Accepted Answer

Let $ x $ be distance from $ +15 \, \mu\text{C} $, then $ 0.75 - x $ from $ -5 \, \mu\text{C} $. $ \frac{15 \times 10^{-6}}{x^2} = \frac{5 \times 10^{-6}}{(0.75 - x)^2} $, $ 15 (0.75 - x)^2 = 5 x^2 $. $ 3 (0.5625 - 1.5 x + x^2) = x^2 $, $ 1.6875 - 4.5 x + 3 x^2 = x^2 $. $ 2 x^2 - 4.5 x + 1.6875 = 0 $, $ x = \frac{4.5 \pm \sqrt{20.25 - 13.5}}{4} = \frac{4.5 \pm 2.6}{4} $. $ x = 0.475 \, \text{m} $ (between charges).

Question 2

A thin spherical shell of radius 10 cm has a charge of $ 8 \, \mu\text{C} $. What is the electric field at a point 5 cm from the center?

Accepted Answer

Inside a thin spherical shell ($ r < R $), $ E = 0 $ (Gauss’s law). Here, $ r = 5 \, \text{cm} < R = 10 \, \text{cm} $, so $ E = 0 \, \text{N/C} $.

Question 3

What causes the electric field to be stronger near a sharp point on a charged conductor compared to a flat surface?

Accepted Answer

Charge concentrates more at sharp points due to lower surface area, increasing the surface charge density. Since the field just outside a conductor is proportional to this density, the field is stronger near points than on flatter regions.

NEET Physics: Electric Charges and Fields — Practice Set 20

Q1. Two charges \( +15 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) are 75 cm apart. What is the distance from \( +15 \, \mu\text{C} \) where the electric field is zero?

Q2. A thin spherical shell of radius 10 cm has a charge of \( 8 \, \mu\text{C} \). What is the electric field at a point 5 cm from the center?

Q3. What causes the electric field to be stronger near a sharp point on a charged conductor compared to a flat surface?

Q4. An infinite line charge has \( \lambda = 1.5 \times 10^{-6} \, \text{C/m} \). What is the electric field at 50 cm?

Q5. What causes electric field lines to emerge perpendicularly from the surface of a charged conductor?

Q6. A plane sheet has a surface charge density \( \sigma = 1.77 \times 10^{-10} \, \text{C/m}^2 \). What is the electric field near it?

Q7. A closed surface has a net flux of \( 9.04 \times 10^5 \, \text{Nm}^2/\text{C} \). What is the charge enclosed?

Q8. Why does the electric field remain constant inside a region where field lines are uniformly spaced and parallel?

Q9. Three charges \( +2 \, \mu\text{C} \) each are at the vertices of an equilateral triangle of side 2 m. What is the force on one charge?

Q10. A uniform electric field \( E = 8 \times 10^3 \, \text{N/C} \) is along the x-axis. What is the flux through a rectangle of 20 cm × 30 cm in the yz-plane?