Electric Charges And Fields

Step 1: Concept
Potential .
Step 2: Analysis
On the axial line, or , so .
Step 3: Conclusion
This yields the maximum magnitude of potential for a given distance.
Final Answer: (A)

Step 1: Concept
Work .
Step 2: Analysis
Case 1: . Thus, . Case 2: .
Step 3: Conclusion
.
Final Answer: (B)

Step 1: Properties of Group 1
Alkali metals are the most electropositive elements in their respective periods.
Step 2: Analysis
They have the largest atomic radii and effectively shield their valence electrons.
Step 3: Ionization Energy
Because they lose their valence electron easily, they possess the minimum (low) ionization energy in their period, not high.
Step 4: Verification
Options (b), (c), and (d) are true characteristics of alkali metals.
Final Answer: (a)

Step 1: Calculate Atoms of 'A'
Atoms at corners are shared by 8 unit cells. Number of A atoms .
Step 2: Calculate Atoms of 'B'
Atoms at face centers are shared by 2 unit cells. There are 6 faces. Number of B atoms .
Step 3: Empirical Formula
The ratio of A:B is 1:3, leading to the formula .
Final Answer: (d)

Step 1: Analysis
When is added to ( ), the new charge becomes .
Step 2: Calculation
According to Coulomb's Law, force is proportional to the product of charges ( ).
Step 3: Conclusion
Since one of the charges is now zero, the force becomes zero.
Final Answer: (b)

Step 1: Use the relation between radius and electric force.
The force on an oil drop is given by: where is the potential difference, is the charge, and is the distance between the plates. The force on the drop is also related to the radius by: Since the radius is halved, the new force will be of the original force.

Step 2: Relate the new potential difference.
The new potential difference is proportional to the change in force: Thus, the charge on the second drop is .

Step 1: Calculate the electric force.
The force acting on the oil drop is the electric force, given by: where is the charge on the drop, and is the electric field between the plates. The electric field is: where is the potential difference and is the distance between the plates. Substituting the given values:

Step 2: Set up the balance of forces.
The oil drop is stationary, so the electric force is balanced by the gravitational force: The gravitational force is . Thus: Solving for :

Step 3: Find the number of electrons.
The charge on a single electron is . The number of electrons is:

Step 1: Calculate the current.
The current due to ions is given by: where,
,
.
Hence: Similarly, the current due to electrons: Since electrons move to the left, their current will be considered negative. Adding the ion and electron currents: Thus, the current is towards the right.

Step 2: Conclusion.
The current in the discharge tube is , towards the right, which is option (2).

Step 1: Understanding the Concept:
Relativistic momentum .
Step 2: Detailed Explanation:
When is doubled, denominator becomes smaller than .
So increases by factor more than 2. At non-relativistic speeds, . At relativistic speeds, increases faster than .
Step 3: Final Answer:
Thus, momentum becomes more than double.

Step 1: Understanding the Concept:
Relative acceleration of bolt w.r.t. elevator = (since elevator accelerates upward).
Step 2: Detailed Explanation:
Elevator acceleration upward. Bolt accelerates downward with .
Relative acceleration = .
Initial relative velocity = 0. Distance = .
Using :
.
Step 3: Final Answer:
Thus, time = .

Step 1: Understanding the Concept:
Einstein's mass-energy equivalence: . GWh = J = J.
Step 2: Detailed Explanation:
kg = 1.6 g.
Step 3: Final Answer:
Thus, mass annihilated = 1.6 g.

Concept: Electric field due to infinite sheet: Direction:
• Away from
• Towards

Step 1: Identify sheets
Top:
Middle:
Bottom:

Step 2: Field contributions at
From : downward From : upward From : upward

Step 3: Net field
Conclusion:

Concept: Charging by friction produces static electricity. Moisture (humidity) allows charges to leak away.

Step 1: Effect of wet hair and rain.
Water conducts electricity and prevents charge accumulation.

Step 2: Conclusion.
No static charge develops, so no attraction occurs.

Concept: Current:

Step 1: Given values.


Step 2: Calculate current.

Concept: Electric field of dipole:
• On axial line → along dipole axis
• On equatorial line → opposite to dipole axis

Step 1: Point P.
P lies on axial line field along axis.

Step 2: Point Q.
At symmetric point, perpendicular components cancel, leaving resultant along axis.

Step 3: Conclusion.

Concept: Electric force: gives constant acceleration.

Step 1: Motion analysis.
Acceleration is along electric field, while initial velocity is at an angle.

Step 2: Trajectory.
Motion is analogous to projectile motion.

Concept: Electric potential due to a dipole:

Step 1: Observe dependence on distance.


Step 2: Conclusion.
Thus, potential varies inversely with square of distance.

Concept: Work done in moving charge: Potential due to dipole:

Step 1:Given data
•
•
•

Step 2:Potential difference

Step 3:Substitute values From dipole: Using values from figure and : Conclusion