Electric Charges and Fields NEET Questions

Explanation: This question asks what happens to the Electric Field in a region where electric potential does not vary with position. Electric potential and Electric Field are closely related physical quantities in Electrostatics.

Electric Field is defined as the negative gradient of electric potential. This means the Electric Field depends on how rapidly the potential changes with distance. If the potential remains the same everywhere in a region, there is no change in potential across any direction.

Mathematically, when the spatial rate of change of potential is zero, the gradient becomes zero. Since Electric Field is proportional to this gradient, the field must also vanish. Physically, this means there is no force acting on a charge placed in that region.

For example, inside a conductor in electrostatic equilibrium, the potential is constant throughout. Hence, any charge placed inside does not experience any electric force.

In summary, a constant potential region implies no variation in potential, leading to a zero gradient and therefore no Electric Field present in that region.

Explanation: This problem involves finding the electric potential at a point due to two point charges placed at different positions in space. Electric potential due to a point charge depends on its magnitude and distance from the observation point.

The total potential at any point is obtained by adding contributions from all charges. Each contribution depends inversely on the distance between the charge and the observation point. Since one charge is positive and the other is negative, their effects will partially cancel depending on distances.

To solve this, first determine the distances from the observation point to each charge using Vector distance formula. Then apply the expression for electric potential due to a point charge and add the contributions algebraically, considering their signs.

For instance, if two equal and opposite charges are placed symmetrically, their potentials may cancel at certain points. However, if distances differ, cancellation is incomplete.

Thus, the final potential depends on relative distances and signs of charges, requiring careful Vector distance calculation and algebraic addition of potentials.

Explanation: This question refers to a fundamental concept in Electrostatics related to energy and electric fields. When a charge is moved in an Electric Field, work is required if the motion is against the electric force.

Electric potential at a point is defined as the work done per unit positive charge in bringing it from infinity to that point. Infinity is taken as the reference where potential is assumed to be zero.

To understand this, imagine slowly bringing a charge closer to another charge. If the charges repel, work must be done against the repulsive force. This work gets stored as potential energy in the system.

For example, lifting an object against gravity stores gravitational potential energy. Similarly, moving a charge against electric force stores electric potential energy, which per unit charge defines potential.

In summary, the work done per unit charge in bringing it from infinity to a point defines the electric potential at that location.

Explanation: This question deals with the concept of capacitance of a conducting sphere and how it changes when smaller charged drops combine to form a larger drop.

Capacitance of an isolated spherical conductor depends directly on its radius. When multiple identical drops combine, the total volume is conserved. Since volume is proportional to radius³, combining 64 drops increases the radius of the resulting drop.

Specifically, if 64 identical drops merge, the radius of the new drop becomes 4 times that of a single drop because 64 = 4³. Since capacitance is proportional to radius, the capacitance increases proportionally.

As an analogy, imagine combining small soap bubbles into a larger one—the size increases significantly, and properties depending on size also scale accordingly.

Thus, the ratio of capacitance depends on how the radius changes when multiple identical charged drops combine into one larger drop.

Explanation: This question involves magnetic flux and the geometry of magnetic fields produced by a current-carrying loop. Magnetic flux is defined as the total magnetic field passing through a given surface.

For a circular loop lying in the x–y plane, the magnetic field produced by the current circulates around the wire. According to the right-hand rule, the magnetic field lines form closed loops and are perpendicular to the plane near the center but not uniformly across the plane.

However, when considering the entire infinite plane, the NET magnetic flux becomes zero because the field lines entering and leaving the plane cancel each other out. Magnetic field lines are continuous and do not begin or end.

For example, imagine airflow entering and exiting a flat surface equally; the NET flow across the entire surface is zero.

In summary, due to symmetry and the closed nature of magnetic field lines, the total magnetic flux through the entire plane becomes zero.

Explanation: This question focuses on the energy associated with placing an electric dipole in an external Electric Field under specific conditions.

An equipotential surface is one where the electric potential is the same everywhere. Moving a charge along such a surface requires no work because there is no change in potential energy.

If both charges of a dipole (+q and −q) are always placed on equipotential surfaces during movement, no NET work is done by or against the Electric Field. However, the system still possesses energy due to its configuration in the field.

This energy depends on the orientation of the dipole and its interaction with the external field. It represents stored energy rather than kinetic motion.

In summary, when a dipole is positioned in an electric field while maintaining equipotential conditions, the associated energy arises from its configuration in the field.

Explanation: This question deals with how dielectric materials respond to external electric fields at the Molecular level. Polarisation occurs when charges within molecules shift slightly under an applied electric field.

In dielectrics, the applied electric field induces dipoles or aligns existing dipoles. However, the actual field experienced by a Molecule is not just the external field—it is modified by neighboring molecules and internal interactions.

This effective field acting at the Molecular level is responsible for polarisation. It determines how strongly molecules align or distort under the applied field.

For example, in a crowd, an individual’s movement is influenced not only by an external push but also by nearby people. Similarly, molecules experience a combined effect.

In summary, the field that acts at the Molecular scale and causes polarisation differs from the external field and accounts for internal interactions within the dielectric.

Explanation: This question explores the concept of electric potential due to a point charge and the work involved in bringing another charge close to it.

Electric potential due to a point charge varies inversely with distance from the charge. As the distance decreases, the potential increases significantly. At the exact location of the charge, the distance becomes zero.

Since potential is inversely proportional to distance, it grows without bound as one approaches the charge. This implies that bringing a charge exactly to the position of another point charge requires an unbounded amount of work.

For instance, compressing a spring infinitely would require infinite energy, which is not physically achievable. Similarly, bringing charges to zero separation leads to extreme energy requirements.

In summary, due to the inverse dependence on distance, the work required increases drastically as the separation approaches zero.

Explanation: This question combines the concepts of electric field, force on a charge, and potential difference in a uniform field.

Electric field strength is defined as force per unit charge. Once the field is known, potential difference between two points in a uniform field can be calculated by multiplying the field strength with the distance between the points.

First, determine the electric field using the given force and charge. Then convert the distance into meters and apply the relation between electric field and potential difference.

For example, in a uniform gravitational field, potential difference depends on height difference. Similarly, in an electric field, potential difference depends on separation along the field direction.

In summary, the problem involves finding field strength from force and charge, then using distance to determine the resulting potential difference.

Explanation: This question examines the motion of a charged particle under the influence of an electric field when its initial velocity is not aligned with the field.

An electric field exerts a force on a charged particle in a fixed direction. If the particle already has velocity in another direction, its motion becomes a combination of uniform motion and accelerated motion.

This is similar to projectile motion, where horizontal velocity remains constant while vertical motion is affected by gravity. In this case, the electric field plays the role of gravitational acceleration.

Thus, the particle follows a curved trajectory due to the combined effect of initial velocity and constant acceleration in a different direction.

In summary, when velocity and electric field are not aligned, the particle undergoes motion similar to projectile motion, resulting in a curved path.

Explanation: This question compares electric force and gravitational force acting on an electron and asks for the condition when they are equal.

The electric force on a charge is given by the product of charge and electric field, while the gravitational force is given by Mass times gravitational acceleration.

To find the required electric field, equate these two forces. This gives a relation involving the Mass and charge of the electron and gravitational acceleration.

For example, balancing two forces like tension and weight helps determine equilibrium conditions. Similarly, here the electric force balances the weight of the electron.

In summary, by equating electric and gravitational forces, one can derive the expression for the electric field needed to balance the electron’s weight.

Explanation: This question involves understanding how electric fields behave due to point charges and how magnitude and direction vary with charge values.

Electric field due to a point charge depends on the magnitude of the source charge and the distance from it. It is directly proportional to the charge and inversely proportional to the square of distance.

At the location of one charge, the field is due to the other charge. Since the charges differ in magnitude, the field strengths will also differ accordingly. Direction also plays a role because one charge is positive and the other is negative.

For example, a stronger charge produces a stronger field at the same distance. Similarly, reversing the sign changes direction but not magnitude.

In summary, the electric field at each charge depends on the magnitude and sign of the other charge, requiring proportional reasoning and direction consideration.

Explanation: This question explores the condition for electrostatic equilibrium in a system of charges arranged symmetrically. Equilibrium means that the NET force on each charge is zero.

When two equal charges are placed symmetrically and a third charge is introduced at the center, the forces acting on each charge must balance. The central charge experiences equal and opposite forces from the two outer charges due to symmetry.

However, for the outer charges, the forces due to each other and the central charge must cancel. This requires careful balancing of magnitudes and directions using Coulomb’s law. The value and sign of the central charge determine whether it attracts or repels the outer charges.

For instance, placing a weight between two equal springs requires proper adjustment so that all forces cancel. Similarly, here the charge must be chosen to maintain balance.

In summary, equilibrium is achieved only when forces on all charges cancel, which depends on both magnitude and sign of the central charge.

Explanation: This question relates to the behavior of electric fields inside a uniformly charged hollow spherical shell. This is a standard result derived using Gauss’s law.

According to Gauss’s law, the electric field inside a closed conducting shell depends on the NET charge enclosed within the Gaussian surface. Inside a hollow sphere, any Gaussian surface lies entirely within the shell and encloses no charge.

Since the enclosed charge is zero, the NET electric field inside must also be zero. This holds true for every point inside the hollow sphere, regardless of position.

As an analogy, imagine being inside a perfectly symmetrical structure where influences from all sides cancel out. Similarly, the electric effects cancel everywhere inside.

In summary, due to symmetry and zero enclosed charge, the electric field inside a uniformly charged hollow sphere remains zero at all points.

Explanation: This question examines how charge redistribution affects the force between conductors. When two conducting spheres are brought into contact, charges redistribute equally due to identical size.

Initially, the charges are unequal, but after contact, the total charge is shared equally. The new charge on each sphere is determined by averaging the initial charges.

Once separated again, the force between them depends on the new charges and the same distance. Since Coulomb force depends on the product of charges, any change in charge distribution affects the magnitude and nature of force.

For example, mixing two unequal amounts of liquid results in equal portions after redistribution. Similarly, charge gets evenly distributed here.

In summary, contact equalizes charge, and the resulting force depends on the new equal charges and their interaction at the same separation.

Explanation: This question involves summing the contributions of an infinite series of charges arranged at increasing distances. Electric potential is a scalar quantity, so contributions are added algebraically.

Each charge contributes potential inversely proportional to its distance from the origin. As the distances increase geometrically, the contributions decrease correspondingly.

Since the charges alternate in sign, the series becomes an alternating series. Such series often converge to a finite value when the terms decrease sufficiently fast.

For example, adding decreasing positive and negative terms like 1 − 1/2 + 1/4 − 1/8 forms a converging pattern. Similarly, potentials here follow a converging alternating series.

In summary, the total potential is obtained by summing an infinite alternating series of decreasing magnitude terms, leading to a finite result.

Explanation: This question connects electric potential with electric field using their mathematical relationship. Electric field is the negative gradient of potential.

Since the potential depends only on x, the electric field will have a component only along the x-direction. The magnitude of the field is obtained by differentiating the potential with respect to x.

The derivative of x² gives a linear dependence on x, meaning the field varies with position. The negative sign indicates direction opposite to increasing potential.

For example, slope of a hill determines how steep it is; similarly, the rate of change of potential determines field strength.

In summary, by taking the spatial derivative of the given potential function, the direction and magnitude of the electric field can be determined.

Explanation: This question deals with how a medium affects electrostatic force between charges. Coulomb’s law states that force depends on the permittivity of the medium.

In a vacuum, the force is maximum because there is no reduction due to material properties. When a dielectric medium is introduced, the permittivity increases, reducing the effective force between charges.

The reduction factor is equal to the dielectric constant of the medium. Thus, the force becomes smaller compared to its value in vacuum.

For example, sound travels differently in air and water due to medium properties. Similarly, electric interactions are modified by the surrounding medium.

In summary, introducing a dielectric reduces the electrostatic force by a factor equal to the dielectric constant of the medium.

Explanation: This question studies motion of a charge under the influence of two fixed charges placed symmetrically. The forces acting on the moving charge depend on its position relative to both charges.

At the starting point, the forces due to the two charges have components that combine in a specific direction. As the charge moves, both magnitude and direction of forces change continuously.

Although symmetry exists, the restoring force is not directly proportional to displacement at all positions, which is required for simple harmonic motion.

For example, a pendulum exhibits simple harmonic motion only for small angles; beyond that, motion becomes complex. Similarly, here motion is oscillatory but not strictly simple harmonic.

In summary, due to varying force magnitude and direction, the motion is oscillatory but does not satisfy the strict conditions for simple harmonic motion.

Explanation: This question relates to Electrostatics of conductors in equilibrium. In a conducting sphere, charges reside only on the surface, and the interior remains field-free.

Since the electric field inside a conductor is zero, there is no potential difference between any two points inside it. This means the potential remains constant throughout the interior.

Thus, the potential at the center must be the same as the potential at the surface. This is a direct consequence of electrostatic equilibrium.

For example, in a still water tank, pressure at the same depth remains constant. Similarly, potential inside a conductor remains uniform.

In summary, zero electric field inside a conductor ensures uniform potential throughout, including at the center.

Explanation: This question involves the photoelectric effect and its influence on a charged object in an electric field. High-energy X-rays can eject electrons from a metal surface.

When electrons are emitted, the ball loses negative charge and may become positively charged. The electric field then exerts a force on this newly charged object.

The direction of motion depends on the nature of the acquired charge and the direction of the electric field. Since force equals charge times electric field, any change in charge alters the motion.

For example, removing electrons from a body is like reducing weight on one side, causing imbalance and movement.

In summary, X-ray exposure changes the charge of the ball, and the electric field then causes it to move accordingly.

Explanation: This question tests understanding of electrostatic interactions between charged and neutral bodies. Like charges repel, unlike charges attract, and neutral bodies can be attracted due to induction.

Given multiple interactions, one must analyze which combinations imply similar or opposite charges. Repulsion confirms both objects are charged with the same sign, while attraction may indicate opposite charges or a charged-neutral interaction.

By carefully comparing all given pair interactions, one can deduce the nature of each ball’s charge. Logical elimination helps identify the possible charge on ball 1.

For example, solving puzzles with clues requires eliminating inconsistent possibilities. Similarly, here interactions act as clues.

In summary, analyzing attraction and repulsion patterns allows deduction of the charge nature of the given ball through logical reasoning.

Explanation: This question focuses on how the presence of a dielectric medium alters the electrostatic force between two charges. The force between charges in a vacuum or air is governed by Coulomb’s law.

When a dielectric medium is introduced, the permittivity of the medium increases compared to vacuum. This reduces the effective electric field between the charges and consequently reduces the force of interaction.

The reduction factor is directly related to the dielectric constant of the medium. The new force becomes inversely proportional to this constant, meaning a higher dielectric constant leads to a greater reduction in force.

For example, interactions between objects feel weaker in water compared to air due to medium effects. Similarly, electric forces are reduced in materials with higher dielectric constants.

In summary, introducing a dielectric medium weakens the electrostatic force, with the extent of reduction determined by the dielectric constant of the medium.