Two long current carrying thin wires, both with current , are held by insulating threads of length and are in equilibrium as shown in the figure, with threads making an angle with the vertical. If wires have mass per unit length then, the value of is :
( gravitational acceleration)
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Official Solution
Correct Option: (1)
02
PYQ 2022
medium
physicsID: jee-main
A long cylindrical volume contains a uniformly distributed charge of density ρ. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is:
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3
4
Official Solution
Correct Option: (1)
⇒
03
PYQ 2022
medium
physicsID: jee-main
If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be:
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4
Official Solution
Correct Option: (2)
Total flux passing through the flat surface:
So
04
PYQ 2022
medium
physicsID: jee-main
Three point charges of magnitude , and are located at the vertices, of a right angled triangle whose sides are cm, cm and cm and point A is the right angle corner. Charge at point A, experiences ______N of electrostatic force due to the other two charges.
Official Solution
Correct Option: (1)
=
=
05
PYQ 2023
hard
physicsID: jee-main
Considering a group of positive charges, which of the following statements is correct ?
1
Net potential of the system cannot be zero at a point but net electric field can be zero at that point.
2
Net potential of the system at a point can be zero but net electric field can't be zero at that point.
3
Both the net potential and the net electric field cannot be zero at a point.
4
Both the net potential and the net field can be zero at a point.
Official Solution
Correct Option: (1)
Here , and are positive Therefore V > 0 So , the correct option is (A) : Net potential of the system cannot be zero at a point but net electric field can be zero at that point.
06
PYQ 2023
hard
physicsID: jee-main
An electron revolves around an infinite cylindrical wire having uniform linear charge density in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ____ . Given mass of electron = kg.
Official Solution
Correct Option: (1)
To determine the velocity of the electron, we follow these steps: 1. Electric Field due to an Infinite Cylindrical Wire: The electric field at a distance from an infinite wire with linear charge density is given by: where is the permittivity of free space ( C /N·m ). 2. Force on the Electron: The electrostatic force acting on the electron is: where is the charge of the electron ( C). 3. Centripetal Force: For the electron to move in a circular path, the electrostatic force must provide the necessary centripetal force: Equating the two expressions for : Simplifying, we get: 4. Substitute the Given Values: Plugging in the values: Final Answer The velocity of the electron is m/s.
07
PYQ 2023
hard
physicsID: jee-main
A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries as sinusoidally varying current of amplitude 2.5 A and angular frequency 700 rad s–1. The central axes of the loop and selenoid coincide. The amplitude of the emf induced in the loop is x×10–4 V . The value of x is ______ . (Take, = 22/7)
Official Solution
Correct Option: (1)
Step 1: Understanding the induced emf in a loop inside a solenoid.
The induced emf in the loop is given by the equation:
Where:
- is the magnetic field in the solenoid,
- is the area of the loop,
- is the angular frequency of the solenoid's current,
- is the number of turns per unit length. Step 2: Calculating the magnetic field in the solenoid.
The magnetic field inside a solenoid is given by:
Where:
- ,
- ,
- . So, the magnetic field is:
Step 3: Area of the loop. The area of the loop is:
Step 4: Calculating the induced emf. Substitute the values into the equation for emf:
08
PYQ 2023
medium
physicsID: jee-main
The number density of free electrons in copper is nearly 8 \times 1028 m-3. A copper wire has its area of cross section = 2 \times 10-6 m² and is carrying a current of 3.2 A. The drift speed of the electrons is _____ \times 10-6 ms-1
Official Solution
Correct Option: (1)
The drift velocity ( ) is given by: where: , (number density), (charge of an electron), (cross-sectional area). Rearrange to solve for : Substitute the values: Simplify: Final Answer: The drift velocity is:
09
PYQ 2023
medium
physicsID: jee-main
Equivalent resistance of the following circuit (in ohms) is equal to . Value of x is equal to _____.
Official Solution
Correct Option: (1)
Let's analyze the circuit step-by-step to calculate the equivalent resistance between points A and B.
Simplify the top two resistors: The two 8-ohm resistors are in series. Their combined resistance is 8 Ω + 8 Ω = 16 Ω.
Simplify the two 4-ohm angled resistors: The two 4-ohm resistors connected to the terminals of 8 ohm resistors are also in series. The combined resistance is 4 Ω + 4 Ω = 8 Ω.
Simplify the three 4-ohm and combined resistors: The combined 16-ohm resistor, the combined 8-ohm resistor and the 4-ohm resistor are connected in parallel. The formula for parallel resistors is 1/Req = 1/R1 + 1/R2 + 1/R3 , so, 1/Req = 1/16 + 1/8 + 1/4= (1+2+4)/16 = 7/16 The equivalent resistance is Req =16/7
Given that the equivalent resistance is x/7 ohms and calculated equivalent resistance is 16/7, so the value of x is 16.
10
PYQ 2023
medium
physicsID: jee-main
A point charge is placed at origin. Another point charge is placed at . Charge of proton is q0. The proton is placed on x axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is _____ cm.
Official Solution
Correct Option: (1)
Force Balance Condition: - The electrostatic force on the proton is zero when:
Using Coulomb’s law:
Simplify: - Cancel and :
Take the square root:
Cross-multiply:
Solve for :
Position of Proton: - The proton is from the origin.
Final Answer: 24 cm
11
PYQ 2024
medium
physicsID: jee-main
Two charged particles A and B have charge q each while masses are & . Both have the same velocity v and enter into a transverse magnetic field B such that their radii are & . Then the ratio is
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4
Official Solution
Correct Option: (3)
The correct option is (C):
12
PYQ 2024
medium
physicsID: jee-main
Two charges q and 3q are placed at a distance r from each other. Find the distance from q where the electric field is zero.
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Official Solution
Correct Option: (1)
The Correct Option is (A) :
13
PYQ 2024
hard
physicsID: jee-main
A solid sphere of radius units is placed with its centre at origin. Two charges at and at is placed. If the flux through the sphere is , find
Official Solution
Correct Option: (1)
Step 1: Use Gauss's Law.
According to Gauss's law: That means the electric flux through any closed surface depends only on the net charge enclosed by that surface.
Step 2: Identify which charges are enclosed within the sphere.
The sphere is centered at the origin with radius , so its surface extends from:
Now check the given charges:
Charge is at : outside the sphere (since ).
Charge is at : inside the sphere (since ).
Hence, the net enclosed charge inside the sphere:
Step 3: Apply Gauss’s law.
So, comparing with given expression: We get:
Final Answer:
14
PYQ 2024
hard
physicsID: jee-main
Two charges and are kept in a line separated by a distance . Electric field is zero at a distance x from . Find the value of .
Official Solution
Correct Option: (1)
The Correct Answer is :
15
PYQ 2024
hard
physicsID: jee-main
Find the ratio of the charge on to that on in steady state.
Official Solution
Correct Option: (1)
The correct answer is : 3
16
PYQ 2024
easy
physicsID: jee-main
An electron is moving with the speed of at a distance of , from a large sheet of charge with density . Find the maximum value of such that electron hits the sheet after . (mass of electron = kg, Permittivity of free space =
Official Solution
Correct Option: (1)
17
PYQ 2026
medium
physicsID: jee-main
Six point charges are kept apart from each other on the circumference of a circle of radius as shown in figure. The net electric field at the center of the circle is ___________. ( is permittivity of free space)
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Official Solution
Correct Option: (2)
Each charge is placed at a distance from the center. The magnitude of electric field due to a charge at the center is
Step 1: Analyze symmetry of charge distribution. From the figure, the charges are placed at angular separations of . Due to symmetry, electric field vectors due to opposite charges partially cancel each other. Hence, we resolve the electric field vectors along the -axis and -axis. Step 2: Resolve horizontal components. Considering the directions of electric field due to each charge,
the net horizontal component is proportional to
Step 3: Resolve vertical components. Similarly, the net vertical component is proportional to
Step 4: Write the resultant electric field vector. Combining both components,
Final Answer:
