Over 100 Electrostatics MCQs | Physics MCQs

In electrostatic equilibrium, the net electric field inside any conductor is zero. Any field would cause the free charges to move until the field is canceled out.

Since the electric field inside is zero, no work is done moving a charge from the surface to any point inside. Therefore, the potential is constant throughout the conductor and equal to the potential at its surface.

An electric field has both magnitude (strength) and direction, making it a vector quantity. The others are scalar quantities.

According to Coulomb's law, force is inversely proportional to the square of the distance (F ∝ 1/r²). If the distance is doubled (2r), the force becomes 1/(2r)² = 1/4 of the original force. 120 N / 4 = 30 N.

According to Newton's third law, the forces two objects exert on each other are always equal in magnitude and opposite in direction. This action-reaction pair applies to electrostatic forces as well.

This unit can be derived from the Coulomb's law formula, F = (1/4πε₀)(q₁q₂/r²). Rearranging for ε₀ gives its units as C² / (N·m²).

First, find the equivalent capacitance for a parallel combination: C_eq = C1 + C2 = 10 μF + 20 μF = 30 μF. Then, find the total charge using Q_total = C_eq * V = (30 x 10⁻⁶ F) * (6 V) = 180 x 10⁻⁶ C, or 180 μC.

The force on a charge is F = qE. Since an electron's charge (q) is negative, the force vector will be in the opposite direction to the electric field vector.

The potential inside a charged conductor is constant and equal to the potential on its surface. Since the charge is positive, the potential will be positive.

Charging by induction involves redistributing the charge on an object by bringing a charged object nearby, and then using a ground connection to remove some of that charge.

An electroscope is a simple device used to detect the presence and sign of an electric charge by observing the repulsion of its thin metallic leaves.

Work done (W) is the charge (q) multiplied by the potential difference (ΔV). W = q(V_final - V_initial) = 4 C * (15 V - 10 V) = 4 C * 5 V = 20 J.

Positive potential energy implies a repulsive force. Work must be done on the system to bring two like charges (both positive or both negative) together. Option 2 is also correct, but typically only one is listed.

The formula for electric potential is V = kq/r. This shows that potential (V) is inversely proportional to the distance (r) from the point charge.

By definition, capacitance is C = Q/V. If C = 1 F and Q = 1 C, then V must be 1 V.

Photocopiers use a process called xerography, which relies on electrostatics to attract charged toner particles to a photosensitive drum that has been exposed to an image.

Use the electric field formula: E = k * |q| / r². Convert charge to Coulombs: q = 2 x 10⁻⁹ C. Then, E = (9 x 10⁹) * (2 x 10⁻⁹) / 3² = (9 x 10⁹) * (2 x 10⁻⁹) / 9 = 2 N/C.

In an inkjet printer, tiny ink droplets are given an electric charge and then passed through deflecting plates. The electric field between the plates directs the droplets precisely onto the paper.

Relative permittivity (or dielectric constant) K = ε / ε₀, where ε is the permittivity of the medium and ε₀ is the permittivity of free space (a vacuum).

Use the energy formula for a capacitor: U = 0.5 * C * V². Convert capacitance to Farads: C = 200 x 10⁻⁶ F. Then, U = 0.5 * (200 x 10⁻⁶ F) * (50 V)² = 0.5 * (200 x 10⁻⁶) * 2500 = 0.25 J.

Since the electric field inside a conductor is zero, the dielectric constant, which represents the factor by which an external field is reduced, is considered to be infinite.

For a uniform electric field, the potential difference is ΔV = E * d. So, ΔV = 1000 N/C * 0.02 m = 20 V.

Electric flux (Φ) is the product of the electric field (E, in N/C) and the perpendicular area (A, in m²). Thus, its unit is N·m²/C. Option 3, V·m, is also a correct unit for electric flux.

A lightning rod provides a low-resistance path to the ground. The sharp point concentrates the electric field, ionizing the air and creating a conductive path for the lightning strike to follow safely to the ground.

The density of electric field lines (how close they are to each other) in a diagram represents the strength of the electric field. Closer lines indicate a stronger field.

Robert Millikan's experiment involved balancing the gravitational and electric forces on tiny charged oil droplets to calculate the charge of a single electron, proving that charge is quantized.

The elementary charge, which is the charge of a single proton or the magnitude of the charge of a single electron, is approximately 1.602 x 10⁻¹⁹ Coulombs.

Good electrical conductors, like metals, have a sea of delocalized electrons that are free to move throughout the material, allowing for the easy flow of electric current.

Grounding (or earthing) provides a path for charge to flow to or from the Earth, which acts as a massive reservoir of charge, effectively neutralizing the object.

For series capacitors, 1/C_eq = 1/C₁ + 1/C₂ + 1/C₃ = 1/2 + 1/3 + 1/6 = (3+2+1)/6 = 6/6 = 1. Therefore, C_eq = 1 F.

The capacitance of a capacitor with a dielectric is C' = K * C, where C is the original capacitance and K is the dielectric constant of the material.

The electric field vector at any point is always perpendicular to the equipotential surface passing through that point. This is because no work is done moving along an equipotential surface.

For a uniform field, E = V / d. Convert distance to meters: d = 0.02 m. Then, E = 40 V / 0.02 m = 2000 N/C.

Force is proportional to 1/r². If r becomes r/2, the new force is proportional to 1/(r/2)², which is 1/(r²/4) or 4/r². The force becomes four times larger.

The polarized dielectric creates an internal electric field that opposes the external field from the plates, reducing the net electric field between them.

It works by using a moving belt to accumulate electric charge on a hollow metal globe, building up a very high electrostatic potential (voltage).

Michael Faraday, a brilliant experimentalist, introduced the concept of lines of force as a visual and conceptual tool to understand electric and magnetic phenomena.

The electric field is the negative gradient of the electric potential. This means the field points in the direction of the steepest decrease in potential. E = V/d is a special case for uniform fields.

This is the precise definition of an electric dipole, a common configuration found in molecules like water.

Use the capacitance formula: Q = C * V. First, convert capacitance to Farads: C = 5 x 10⁻⁶ F. Then, Q = (5 x 10⁻⁶ F) * (12 V) = 60 x 10⁻⁶ C, which is 60 μC.

The torque is given by τ = pE sin(θ). The sine function is maximum (value of 1) when the angle θ is 90 degrees, meaning the dipole is perpendicular to the field.

Potential energy is U = -pE cos(θ). The cosine function is maximum (value of 1) at 0 degrees, making the potential energy most negative (minimum). This is the stable equilibrium position.

Gauss's Law requires the use of a hypothetical closed surface, called a Gaussian surface, to relate the flux through it to the charge enclosed within it.

According to Gauss's Law, the net flux is proportional to the enclosed charge (Φ = Q_enc / ε₀). If the enclosed charge is zero, the net flux must also be zero.

A positive charge naturally moves from high potential to low potential, so the field does positive work, and the charge loses potential energy.

An electron-volt is the amount of kinetic energy gained by a single electron when it accelerates through a potential difference of one volt. 1 eV = 1.602 x 10⁻¹⁹ Joules.

Using the formula for the capacitance of an isolated sphere, C = 4πε₀R, the value is approximately 711 x 10⁻⁶ Farads, or 711 microfarads.

For a uniform electric field, where the field lines are parallel and equally spaced, the equipotential surfaces are planes that are perpendicular to the field lines.

The charged body induces a separation of charge (polarization) in the neutral object, bringing opposite charges closer and like charges farther away, resulting in a net attractive force.

The time constant (τ = RC) represents the time required for the voltage across a charging capacitor to reach approximately 1 - 1/e, or 63.2%, of its final value.

The negative charges distribute over the surface and repel each other. This mutual repulsion creates an outward pressure that causes the soap bubble to expand.

The principle of quantization states that any observable charge is an integer multiple of the elementary charge, e (the charge of one electron or proton).

Dielectric strength is an intrinsic property of an insulating material that defines the maximum electric field it can sustain before it loses its insulating properties and becomes conductive (breaks down).

The electric dipole moment (p) is a vector quantity defined as p = qd, where q is the magnitude of the charge and d is the separation distance. Its unit is therefore Coulomb times meter.

Use the work-potential formula: W = q * (V_final - V_initial). Here, q = 3 x 10⁻⁹ C and the potential difference is 80 V - 20 V = 60 V. So, W = (3 x 10⁻⁹ C) * (60 V) = 180 x 10⁻⁹ J, or 180 nJ.

Using Gauss's Law, it can be shown that the electric field from an infinite sheet of charge is uniform (E = σ/2ε₀), and thus does not change with distance from the sheet.

Capacitive reactance is Xc = 1/(2πfC). For DC, frequency f=0, so Xc is infinite (acting as an open circuit). For AC, f > 0, so Xc is finite, allowing current to 'pass'.

Surface charge density (σ) is used to describe the distribution of charge over a surface and is calculated as σ = Q/A, where Q is the total charge and A is the surface area.

In a parallel connection, the voltage (V) across both capacitors is the same. Since Q = CV, we have Q₁ = C₁V and Q₂ = C₂V. The ratio Q₁/Q₂ = (C₁V)/(C₂V) = C₁/C₂.

This fundamental equation, derived from Maxwell's equations, links the constants of electricity (ε₀) and magnetism (μ₀) to the speed of light, showing that light is an electromagnetic wave.

A Faraday cage works because an external electric field causes the charges within the conductor to redistribute, creating an opposing field that exactly cancels the external field inside the cage.

The energy density stored in an electric field is given by u = ½ε₀E². This shows that energy is stored in the field itself and its density is proportional to the square of the field strength.

In triboelectric charging, certain materials have a higher affinity for electrons. Silk has a higher affinity than glass, so it pulls electrons from the glass, leaving the glass with a net positive charge.

This is the definition of electric field strength (E = F/q). It describes the force that would be exerted on a standard test charge at a certain point in space.

The particle experiences a constant force (and thus constant acceleration) in one direction, while its velocity component perpendicular to the field remains constant. This is analogous to projectile motion under gravity, which results in a parabolic path.

By convention, field lines show the direction of force on a positive test charge. A positive point charge would repel a positive test charge, so the field lines point radially away from it in all directions.

When the electric field is strong enough (exceeding the material's dielectric strength), it can rip electrons from their atoms, creating free charges and causing the insulator to conduct current. This is dielectric breakdown.

For series capacitors: 1/C_eq = 1/C + 1/C + 1/C = 3/C. Inverting this gives C_eq = C/3.

For parallel capacitors, the equivalent capacitance is the sum of the individual capacitances: C_eq = C + C + C = 3C.

This describes the discharging process of an RC circuit. The rate of discharge is proportional to the remaining charge, which mathematically leads to an exponential decay.

Use the electric potential formula: V = k * q / r. Convert units: q = -8 x 10⁻⁹ C and r = 0.5 m. Then, V = (9 x 10⁹) * (-8 x 10⁻⁹) / 0.5 = -72 / 0.5 = -144 V.

It can be charged by direct contact with a charged object (conduction) or by using a nearby charged object and a ground connection to induce a net charge (induction).

The car's metal body acts as a Faraday cage, causing the electric charge from the lightning to flow around the outside of the vehicle to the ground, protecting the occupants inside.

Away from the edges, the electric field lines between two large parallel plates are parallel and equally spaced, indicating a uniform field strength and direction.

A high dielectric constant indicates that a material is a very good insulator that can effectively reduce the electric field passing through it, making it ideal for use in capacitors.

The principle of conservation of energy applies to all isolated systems, including systems of electric charges. Energy can change form (e.g., potential to kinetic), but the total amount remains constant.

This is the definition of a conservative force. The work done in moving a charge between two points depends only on the start and end points, not the path followed, which allows for the definition of electric potential energy.

The potential difference is ΔV = -E⋅d, where d is the displacement vector. The potential changes only when moving parallel to the field lines.

The electric field at any single point in space must have a unique direction and magnitude. If lines crossed, it would imply two different directions for the force at that single point, which is a physical impossibility.

Triboelectric charging, or charging by friction, is the process where electrons are transferred from one material to another through rubbing, based on their electron affinity.

Resistivity is the measure of how strongly a material opposes the flow of electric current. Good conductors, like copper, have very low resistivity.

Resistivity (ρ) is an intrinsic property of a material. It relates resistance (R), length (L), and cross-sectional area (A) by the formula R = ρL/A, giving it units of Ω·m.

At sharp points on a conductor, the charge concentration is very high, creating an intense electric field that can be strong enough to ionize the surrounding air or fluid, causing a discharge.

For capacitors in series, the formula is 1/C_eq = 1/C1 + 1/C2 + 1/C3. So, 1/C_eq = 1/2 + 1/4 + 1/4 = 0.5 + 0.25 + 0.25 = 1. Therefore, C_eq = 1 F.

Mica is a stable mineral that is an excellent electrical insulator with a high dielectric strength, making it a common choice for use in capacitors and other electronic components.