This question assesses understanding of electrostatics and electric fields in the context of charged cell sorting. Electrostatics involves Newton's second law applied to charged particles, where the acceleration is given by a = F/m = qE/m for a charge in an electric field. In this setup, a cell with fixed charge q and mass m experiences only the electric force. Choice A is correct because the acceleration magnitude a = |q|E/m increases linearly with electric field strength E, since q and m are constant. Choice B is incorrect because it suggests that stronger fields reduce force through screening, which contradicts the direct proportionality F = qE and confuses screening effects with field strength effects. When analyzing charged particle dynamics, always apply Newton's second law with the electric force to find that acceleration is directly proportional to field strength.

This question assesses understanding of electrostatics and electric fields in the context of charged droplets in an aerosol. Electrostatics involves the fundamental principle that like charges repel and opposite charges attract, with forces acting along the line joining the charges. In this setup, both droplets carry negative charge (-1.0 nC each), making them like charges. Choice B is correct because like charges (both negative) repel each other, with the force directed along the line connecting the droplets as required by Coulomb's law. Choice A is incorrect because it misapplies the concept of opposites, claiming that negative is opposite to negative, which is a fundamental error in understanding charge interactions. When analyzing electrostatic interactions, always remember that charges of the same sign repel regardless of whether they are positive or negative.

This question assesses understanding of electrostatics and electric fields in the context of a capacitor-based sensor at fixed charge. Electrostatics involves the relationship between charge, field, and geometry in capacitors, where for parallel plates E = σ/ε₀ = Q/(ε₀A) when charge is fixed. In this setup, the capacitor holds constant charge Q while the plate separation d changes. Choice C is correct because the electric field between parallel plates depends on the surface charge density σ = Q/A, giving E = Q/(ε₀A), which is independent of the plate separation d. Choice B is incorrect because it applies the formula E = ΔV/d, which is valid but ΔV changes when d changes at fixed Q, keeping E constant. When analyzing capacitors at fixed charge, remember that E depends on charge density, not separation, making it invariant to spacing changes.

This question assesses understanding of electrostatics and electric fields in the context of a test charge near a charged residue. Electrostatics involves the study of forces on charges, where F = qE and the force direction depends on both the field direction and the charge sign. In this setup, the field points radially outward and the test charge is negative (-1.6×10⁻¹⁹ C). Choice A is correct because a negative charge in an outward-pointing field experiences a force opposite to the field direction, which is radially inward, with magnitude |q|E. Choice B is incorrect because it states the force is outward, which would only be true for a positive test charge. When analyzing forces on test charges, always consider that negative charges experience forces opposite to the field direction, resulting in attraction toward positive source charges.

This question assesses understanding of electrostatics and electric fields in the context of a charged vesicle between parallel plates. Electrostatics involves the study of forces on charges in electric fields, with F = qE determining both magnitude and direction of the force. In this setup, the vesicle has positive charge and the electric field points downward. Choice B is correct because a positive charge experiences a force in the same direction as the electric field, so with E pointing downward, the vesicle accelerates downward. Choice A is incorrect because it states that positive charges move opposite to the field direction, which is actually the behavior of negative charges. When analyzing motion of charged particles, always remember that positive charges follow the field direction while negative charges move opposite to it.

This question assesses understanding of electrostatics and electric fields in the context of Coulomb's law between trapped microspheres. Electrostatics involves the study of forces between charges, with Coulomb's law stating that the force magnitude is F = k|q₁||q₂|/r², where opposite charges attract and like charges repel. In this setup, one sphere has charge +2.0 nC and the other has -2.0 nC, making them opposite charges. Choice B is correct because opposite charges attract with a force proportional to 1/r², as described by Coulomb's law. Choice A is incorrect because it states they repel and has the wrong distance dependence (proportional to r² instead of 1/r²). When analyzing electrostatic forces, always identify the sign of charges first to determine attraction or repulsion, then apply the 1/r² dependence for force magnitude.

This question assesses understanding of electrostatics and electric fields in the context of a parallel-plate capacitor used in biological applications. Electrostatics involves the study of electric fields between charged surfaces, with the uniform field between parallel plates given by E = ΔV/d. In this setup, the electric field depends on the potential difference and plate separation, not on the plate area for a given voltage. Choice C is correct because when d doubles while ΔV remains constant, the electric field E = ΔV/d becomes half its original value. Choice A is incorrect because it incorrectly states that E is proportional to d, when in fact E is inversely proportional to d at constant voltage. When analyzing parallel-plate capacitors, always use E = ΔV/d for the field magnitude and remember that increasing separation decreases field strength at constant voltage.

This question assesses understanding of electrostatics and electric fields in the context of a charged particle in a microfluidic device. Electrostatics involves the study of forces between charges, with the electric force on a charge given by F = qE, where the force direction depends on the sign of the charge. In this setup, a negatively charged bead experiences a force opposite to the electric field direction, since F = qE and q is negative. Choice B is correct because the electric field points along +x, so the force on the negative charge points along -x, causing acceleration in the -x direction. Choice A is incorrect because it states that negative charges accelerate in the direction of the field, which violates the fundamental principle that negative charges experience forces opposite to the field direction. When analyzing electric forces, always remember that positive charges accelerate parallel to E while negative charges accelerate antiparallel to E.

This question assesses understanding of electrostatics and electric fields in the context of proper unit usage. Electrostatics involves the study of forces between charges, and electric field strength has specific equivalent units. In this setup, the researcher reports a field of 2.0 × 10³ V/m, and we need to identify the equivalent unit. Choice A is correct because N/C (newtons per coulomb) is the fundamental unit for electric field strength and is equivalent to V/m (volts per meter). Choice C is incorrect because J/C (joules per coulomb) is the unit for electric potential (voltage), not electric field. When working with electric fields, remember that E can be expressed as either N/C (force per unit charge) or V/m (potential difference per unit distance).

This question assesses understanding of electrostatics and electric fields in the context of protein motion in axonal electric fields. Electrostatics involves the study of forces between charges, where negative charges experience forces opposite to the electric field direction. In this setup, the field points from outside to inside, and the protein domain is negatively charged. Choice B is correct because a negative charge experiences a force opposite to the electric field, so with an inward field, the force is outward. Choice A is incorrect because it claims negative charges move along the field direction, which would only be true for positive charges. When analyzing forces on charged biomolecules, remember that F = qE gives opposite directions for positive and negative charges.