Two point charges and are placed at a distance apart. Where should a third charge be placed between them, so that the electrical potential energy of the system is minimum?
1
At a distance of from
2
At a distance of from
3
At a distance of from
4
None of the above
Official Solution
Correct Option: (4)
Step 1: Understanding the Concept:
Total potential energy of three charges:
Step 2: Detailed Explanation:
Let charge be at distance from . Then total energy:
For extrema:
Solve:
Check nature: at , second derivative is negative, so energy is maximum (not minimum). Hence, no minimum potential energy exists between the charges. Step 3: Final Answer:
02
PYQ 2016
medium
physicsID: met-2016
A thin dielectric rod of length lies along X-axis. One end is at the origin and the other at ( , 0). A total charge Q is distributed uniformly. What is the potential at point (x, 0) when ?
1
2
3
4
Official Solution
Correct Option: (1)
Step 1: . . Step 2: .
03
PYQ 2016
medium
physicsID: met-2016
Two particles of charges and are at 16 cm away from each other. Where should another charge q be placed between them, so that the system remains in equilibrium?
1
24 cm from
2
12.23 cm from
3
80 cm from
4
6.63 cm from
Official Solution
Correct Option: (4)
To find the position of a charge such that the system remains in equilibrium, we apply the principle that the net force acting on the charge must be zero. Here, one charge is and the other is , separated by a distance of 16 cm.
Let the distance of charge from the charge be , and hence the distance from will be cm.
Using Coulomb's Law, the force on charge due to is given by:
And the force on charge due to is given by:
For equilibrium, these forces must be equal in magnitude:
Cancelling common terms:
Cross-multiplying gives:
Expanding and solving:
Rearranging gives:
Now using the quadratic formula:
, where , , and
Considering the positive root as distance cannot be negative:
Thus, the charge should be placed approximately 6.63 cm from for the system to be in equilibrium.
04
PYQ 2017
easy
physicsID: met-2017
The electric potential is +100 V at a distance of 10 cm from a point charge . Then, is equal to
Official Solution
Correct Option: (1)
05
PYQ 2017
easy
physicsID: met-2017
A charged particle of mass and charge is released from rest in an electric field of magnitude . The kinetic energy of the particle after time second is
Official Solution
Correct Option: (1)
06
PYQ 2017
medium
physicsID: met-2017
Two equal point charges, C are placed at each of the two opposite corners of a square and equal point charges at each of the other two corners. The value of , so that the resultant force on is zero is
1
C
2
C
3
C
4
C
Official Solution
Correct Option: (4)
Step 1: Understanding the Concept:
For the resultant force on to be zero, the attractive force from the two charges must balance the repulsive force from the other . Step 2: Detailed Explanation:
Let side of square . Force between the two 's (diagonal ): along diagonal.
Force from each charge on : along side.
Net force from two 's along diagonal .
For equilibrium:
C C (with factor adjustment). Step 3: Final Answer: C.
07
PYQ 2017
medium
physicsID: met-2017
Two capacitors, one 4 pF and the other 6 pF, connected in parallel, are charged by a 100 V battery. The energy stored in the capacitors is
1
J
2
J
3
J
4
J
Official Solution
Correct Option: (3)
Step 1: Understanding the Concept:
In parallel, . Energy . Step 2: Detailed Explanation:
pF F
Step 3: Final Answer:
Energy stored J.
08
PYQ 2017
medium
physicsID: met-2017
Two equal charges are kept fixed at and along the -axis. A particle of mass and charge is brought to the origin and given a small displacement along the -axis, then
1
the particle executes oscillatory motion
2
the particle remains stationary
3
the particle executes, SHM along -axis
4
the particle executes SHM along -axis
Official Solution
Correct Option: (4)
Step 1: Understanding the Concept:
At the midpoint (origin), the forces from both charges cancel. For displacement along -axis, it is unstable equilibrium; for displacement along -axis, restoring force acts. Step 2: Detailed Explanation:
If displaced along -axis by small , the net force is directed back towards origin (restoring), producing SHM. Along -axis, displacement leads to a repulsive force away from origin (unstable). Step 3: Final Answer:
The particle executes SHM along the -axis.
09
PYQ 2017
medium
physicsID: met-2017
An electric dipole is placed at an angle of 30 with an electric field of intensity N C . It experiences a torque equal to 4 Nm. The charge on the dipole if the dipole length is 2 cm.
1
8 mC
2
4 mC
3
8 C
4
2 mC
Official Solution
Correct Option: (4)
Step 1: Understanding the Concept:
Torque on a dipole: . Step 2: Detailed Explanation:
Step 3: Final Answer:
The charge on the dipole is 2 mC.
10
PYQ 2017
medium
physicsID: met-2017
Force between two identical charges placed at a distance of in vacuum is . Now a slab of dielectric of dielectric constant 4 is inserted between the charges. If the thickness of the slab is , then the force between the charges will become
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Understanding the Concept:
When a dielectric slab is inserted partially between charges, the effective distance changes. A dielectric slab of thickness and dielectric constant is equivalent to an air gap of different effective length for force calculations. Step 2: Detailed Explanation:
Effective distance:
But the correct approach using field superposition gives effective distance
New force:
Step 3: Final Answer:
The force becomes .
11
PYQ 2017
medium
physicsID: met-2017
Two identical air core capacitors are connected in series to a voltage source of 15 V. If one of the capacitors is filled with a medium of dielectric constant 4, the new potential across this capacitor is
1
5 V
2
8 V
3
10 V
4
12 V
Official Solution
Correct Option: (4)
Step 1: Understanding the Concept:
When capacitors are connected in series, the charge on each capacitor is the same. The voltage across each capacitor is . Step 2: Detailed Explanation:
Let the capacitance of each capacitor initially be . After inserting dielectric of constant , capacitance becomes .
For series combination:
Voltage across the air capacitor (capacitance ):
Voltage across dielectric-filled capacitor (capacitance ):
Step 3: Final Answer:
The new potential across the dielectric-filled capacitor is 3 V, and across the air capacitor is 12 V.
12
PYQ 2018
medium
physicsID: met-2018
Small rain drops of the same size are charged to potential volt each. If such drops coalesce to form a single drop, then the potential of the bigger drop is
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: Understanding the Concept:
Volume conservation: . Charge conservation: . Step 2: Detailed Explanation:
Potential of smaller drop: . Potential of bigger drop: . Step 3: Final Answer:
The potential is .
13
PYQ 2018
medium
physicsID: met-2018
The distance between charges and is . The distance at which a third charge should be placed from the second charge in order that it will not experience any force along the line joining the two charges is
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Understanding the Concept:
For net force to be zero, forces from both charges must be equal and opposite. Step 2: Detailed Explanation:
Let the third charge be placed at a distance from the second charge. . Solving gives m from the second charge. Step 3: Final Answer:
The distance is m.
14
PYQ 2018
medium
physicsID: met-2018
At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Understanding the Concept:
For an electric dipole, the electric field falls off faster than that of a point charge. Step 2: Detailed Explanation:
For a dipole, the electric field at a distance along the axial line is for dipole length. Hence, . Step 3: Final Answer:
The electric field varies as .
15
PYQ 2019
medium
physicsID: met-2019
Two capacitors and are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and holds charge Q. The switch is closed. At steady state, the charge on each capacitors will be
1
Q, 2Q
2
Q/3, 2Q/3
3
3Q/2, 3Q
4
2Q/3, 4Q/3
Official Solution
Correct Option: (2)
Step 1: Understanding the Concept:
Charge redistributes with same voltage across both. Step 2: Detailed Explanation:
Total charge = Q
Step 3: Final Answer:
Charges are Q/3 and 2Q/3.
16
PYQ 2019
medium
physicsID: met-2019
A thin metal plate P is inserted halfway between the plates of a parallel plate capacitor of capacitance C in such a way that it is parallel to the two plates. The capacitance now becomes
1
C
2
C/2
3
4C
4
None of these
Official Solution
Correct Option: (1)
Step 1: Understanding the Concept:
Metal plate creates two capacitors in series. Step 2: Detailed Explanation:
Each half has capacitance
Series: Step 3: Final Answer:
Capacitance remains C.
17
PYQ 2019
medium
physicsID: met-2019
A parallel plate capacitor has an electric field of V/m between the plates. If the charge on the capacitor plate is 1 C, the force on each capacitor plate is
1
0.5 N
2
0.05 N
3
0.005 N
4
None of these
Official Solution
Correct Option: (2)
Step 1: Understanding the Concept:
Force on plate . Step 2: Detailed Explanation:
