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Electric Charges and Fields · Question 22

JEE Main 2025 (Online) 2nd April Morning ShiftMCQMedium📈 Topic in 10% papers+4−1
1

A small bob of mass 100 mg and charge +10 is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density ' ' as shown in figure. If string subtends an angle of 45 with the sheet at equilibrium the charge density of sheet will be: (Given, 0 = 8.85 10-12 Fm and acceleration due to gravity, g = 10 ms2) [figure]

  1. 1.77 nC/m2
  2. 0.885 nC/m2
  3. 885 nC/m2
  4. 17.7 nC/m2

Answer

(1) 1.77 nC/m2

Solution

Field of the sheet: E = 2 0 (horizontal)

Equilibrium: T 45 = qE, T 45 = mg

45 = qEmg = 1 q 2 0 = mg

= 2 0 mgq

= 2 8.85 10-12 10-4 1010 10-6

= 1.77 10-9 C/m2 = 1.77 nC/m2

(m = 100 mg = 10-4 kg)

Answer: (1)

JEE Main 2025 (Online) 2nd April Morning Shift

Keep practising — Electric Charges and Fields

2

Consider a circular loop that is uniformly charged and has a radius a 2. Find the position along the positive z-axis of the Cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy plane at the origin :

  1. a
  2. a/2
  3. 0
  4. a/ 2
JEE Main 2025 (Online) 2nd April Evening Shift
3

An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E = E0 i. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

  1. 12 ml2qE0
  2. 2 ml2qE0
  3. 2 mlqE0
  4. 12 2mlqE0
JEE Main 2025 (Online) 29th January Morning Shift
4

Match List - I with List - II. Choose the correct answer from the options given below :

  1. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
  2. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
  3. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
  4. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
JEE Main 2025 (Online) 29th January Morning Shift

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