Electric Charges And Fields

Step 1: Understanding the Concept:
This question asks to identify the fundamental law of electrostatics that describes the force between stationary electric charges.
Step 2: Detailed Explanation:
(A) Ampere's law: Relates the integrated magnetic field around a closed loop to the electric current passing through the loop. It is a fundamental law of magnetostatics.
(B) Ohm's law: States that the current through a conductor between two points is directly proportional to the voltage across the two points ( ). It deals with electric circuits.
(C) Faraday's law of induction: A fundamental law of electromagnetism that predicts how a changing magnetic field will interact with an electric circuit to produce an electromotive force (emf).
(D) Coulomb's law: States that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This is the law that governs the force between electric charges.
Step 3: Final Answer:
The law that describes the force between two electric charges is Coulomb's law. Therefore, option (D) is correct.

Step 1: Understanding the Concept:
The question asks for the value of charge 'q' such that the entire system of three charges is in equilibrium. This means the net force on each of the three charges must be zero. A charge 'q' placed at the center between two equal charges 'Q' will always be in equilibrium by symmetry. The crucial condition is to ensure that the charges 'Q' are also in equilibrium.
Step 2: Key Formula or Approach:
Let the two charges 'Q' be placed at and . The charge 'q' is at the center, . For the system to be in equilibrium, the net force on the charge Q at must be zero. Step 3: Detailed Explanation:
The force exerted by the charge Q at on the charge Q at is: This force is repulsive and acts along the +x direction.
The force exerted by the charge q at on the charge Q at is: For the net force on Q to be zero, this force must be equal in magnitude and opposite in direction to . Therefore, must be attractive, which implies that q and Q must have opposite signs. So, q must be negative.
Setting the sum of forces to zero: Cancel and from both sides: Step 4: Final Answer:
For the entire system of three charges to be in equilibrium, the central charge q must be equal to . Option (B) is correct.

Step 1: Understanding the Concept:
An electric dipole placed in a uniform electric field experiences a torque that tends to align it with the field. The potential energy of the dipole depends on its orientation with respect to the field. Equilibrium occurs when the torque is zero, and stable equilibrium corresponds to the orientation with the minimum potential energy.
Step 2: Key Formula or Approach:
The torque ( ) on a dipole is given by , with magnitude .
The potential energy ( ) of the dipole is given by , with magnitude .
Here, is the angle between the dipole moment and the electric field .
Step 3: Detailed Explanation:
For equilibrium, the net torque must be zero. This occurs when , which means . This condition is met for two angles: and .
To determine stability, we look at the potential energy .
- Stable equilibrium occurs when the potential energy is at a minimum. is minimum when is maximum ( ). This happens when .
- Unstable equilibrium occurs when the potential energy is at a maximum. is maximum when is minimum ( ). This happens when .
Step 4: Final Answer:
The dipole is in stable equilibrium when the potential energy is minimum, which occurs when the angle between and is 0. This means the dipole moment is aligned with the electric field. Option (D) is correct.

Step 1: Understanding the Concept:
A scalar quantity has only magnitude, while a vector quantity has both magnitude and direction. We need to identify which of the given electrical quantities is a vector.
Step 2: Detailed Explanation:
(A) Electric flux ( ): It is the measure of the flow of the electric field through a given area. It is defined by the dot product . The dot product of two vectors results in a scalar. So, electric flux is a scalar.
(B) Electric potential (V): It is the work done per unit charge to move a charge from a reference point to a specific point in an electric field. It is a scalar quantity, representing potential energy per unit charge.
(C) Electric potential energy (U): It is a form of energy and, like all forms of energy, it is a scalar quantity.
(D) Electric intensity: This is another term for the electric field strength ( ). The electric field at a point is defined as the force experienced by a unit positive charge placed at that point. Since force is a vector, the electric field is also a vector, having both magnitude and direction.
Step 3: Final Answer:
Among the given options, only electric intensity (electric field) is a vector quantity. Therefore, option (D) is correct.

Step 1: Understanding the Concept:
This question compares the relative strengths of two fundamental forces: the electrostatic force and the gravitational force. Since the question is general and does not specify the particles, we can calculate the ratio for a common case, such as two protons.
Step 2: Key Formula or Approach:
Let's consider two protons separated by a distance .
The electric force ( ) between them is given by Coulomb's Law: The gravitational force ( ) between them is given by Newton's Law of Gravitation: The ratio is: Step 3: Detailed Explanation:
We use the standard values for the constants:
- Coulomb's constant, N m /C .
- Elementary charge, C.
- Gravitational constant, N m /kg .
- Mass of a proton, kg.
Now, we calculate the ratio: The ratio is of the order of .
Step 4: Final Answer:
The ratio of the electric force to the gravitational force between two protons is on the order of . This demonstrates that the electric force is immensely stronger than the gravitational force at the subatomic level. Option (C) matches this result.

Step 1: Understanding the Concept:
The principle of "quantisation of charge" is a fundamental property of electric charge. It states that electric charge is not continuous but exists in discrete packets.
Step 2: Detailed Explanation:
The principle of quantisation of charge states that the total charge ( ) on any object is always an integer multiple of a basic unit of charge, denoted by . This basic unit is the magnitude of the charge of a single electron or proton ( C).
The formula is: , where is an integer ( ).
Let's evaluate the given options based on this principle:
(A) Charge, which is a fraction of charge on an electron, is not possible: This is a direct consequence of the rule . Since must be an integer, it is impossible for an isolated object to have a charge of, for example, 0.5 or 1.7 . This statement accurately describes quantisation.
(B) A charge cannot be destroyed: This describes the law of conservation of charge, which is a different principle.
(C) Charge exists on particles: This is a true statement, but it is not the meaning of quantisation.
(D) There exists a minimum permissible charge on a particle: This is also a consequence of quantisation (the minimum non-zero charge is ), but option (A) is a more complete and precise statement of the principle. It explains *why* there is a minimum charge and also rules out all non-integer multiples, not just those below the minimum.
Step 3: Final Answer:
The most accurate and comprehensive description of the quantisation of charge among the choices is that charge cannot exist as a fraction of the elementary charge . Therefore, option (A) is the best answer.

Step 1: Understanding the Concept:
Electric field lines are a visual tool used to represent electric fields. They have several properties that convey information about the field and the charges creating it.
Step 2: Detailed Explanation:
Let's examine what information can be obtained from electric field lines:
(A) Field strength: The density of the electric field lines (how close they are to one another) in a region is proportional to the magnitude, or strength, of the electric field in that region. Where the lines are close together, the field is strong; where they are far apart, the field is weak.
(B) Direction: The tangent to an electric field line at any point gives the direction of the electric field vector at that point. The arrowhead on the line indicates the direction of the force that would be exerted on a positive test charge.
(C) Nature of charge: Electric field lines originate from positive charges and terminate on negative charges (or extend to infinity). By observing the pattern of where lines begin and end, we can determine the location and nature (positive or negative) of the source charges.
Since electric field lines provide information about field strength, direction, and the nature of the charge, all the given options are correct.
Step 3: Final Answer:
Electric field lines provide information about all the listed properties. Therefore, option (D) is the correct answer.