- A fixed source charge +Q is at the origin. A small positive test charge is moved from point A at r=0.30m to point B at r=0.60m. Which statement best describes the electric field magnitude at B compared to at A?
Answer: It is one-fourth as large.
Electric fields. Electric fields exist as properties of space around source charges, with magnitude following E = kQ/r² at each point regardless of test charge presence. When the test charge moves from r = 0.30 m to r = 0.60 m (doubling the distance), the field magnitude at the new location is (0.30/0.60)² = 1/4 of the original value. The field exists at both locations whether or not a test charge is there to experience it. Choice D incorrectly suggests the field becomes zero with distance, confusing decreasing magnitude with complete absence. Remember that electric fields extend throughout space, decreasing with distance but never reaching zero.
- Two fixed source charges are on the x axis: +Q at x=−0.20m and +Q at x=+0.20m. Point P is at the origin, where a small positive test charge is placed. Which statement best describes the electric field at P?
Answer: It is zero because the contributions cancel by symmetry.
Electric fields. The electric field at any point is the vector sum of fields from all source charges, existing as a property of space independent of test charges. Each +Q charge creates a field pointing radially outward from itself. At the origin, the left charge creates a field pointing right (+x direction) while the right charge creates a field pointing left (-x direction). Since the charges are equal and equidistant from P, these fields have equal magnitudes but opposite directions, resulting in complete cancellation and zero net field. Choice D incorrectly assumes the field depends on the test charge's sign, missing that fields exist independently. Always analyze symmetry to identify when field contributions cancel.
- A fixed source charge +Q creates an electric field. A test charge is placed at point P a distance r from +Q, then replaced by a test charge of twice the magnitude at the same point. Which statement best describes the electric field at point P after the replacement?
Answer: It is unchanged because it depends only on the source charge and location.
This question tests understanding of electric fields. The electric field is a property of space determined solely by source charges and their positions, existing whether or not any test charge is present. At any point P, the field E = kQ/r² depends only on the source charge Q and distance r, not on any test charge placed there. Replacing the test charge with one of different magnitude does not alter the field at that location. Choice A incorrectly assumes the test charge contributes to the field it experiences, confusing the roles of source and test charges. To avoid this error, always distinguish between source charges (which create fields) and test charges (which experience forces in those fields).
- Two fixed source charges, +Q and −Q, are separated by a distance d on a line, with +Q on the left. Point M is the midpoint. A small positive test charge +q is placed at M to sense the field. Which statement best describes the direction of the net electric field at M due to the source charges?
Answer: It points right, from +Q toward −Q.
This question tests understanding of electric fields. Electric fields from multiple sources add vectorially at each point in space. At the midpoint M between +Q (left) and -Q (right), the positive charge creates a field pointing right (away from +Q), while the negative charge also creates a field pointing right (toward -Q). Both individual fields point in the same direction—to the right—so they add constructively, resulting in a net field pointing right from +Q toward -Q. Choice C incorrectly suggests the field depends on the test charge value, confusing the field (determined by source charges only) with forces on test charges. To find net fields correctly, always determine the direction of each individual field first, then add them vectorially. - A fixed source charge −2Q is at the origin. Point A is at r=0.30m and point B is at r=0.60m from the origin along the same line. A tiny test charge is used only as a probe. Compared to the electric field strength at B, the electric field strength at A is
Answer: four times as large, because E∝1/r2.
Electric fields are properties of space whose magnitude depends only on the source charge magnitude and distance, not on the source charge sign. For a point charge, E = k|Q|/r², so the field strength is inversely proportional to the square of the distance. Since point A is at half the distance of point B (0.30 m vs 0.60 m), the field at A is (0.60/0.30)² = 4 times stronger than at B. Choice A incorrectly suggests the negative sign affects the magnitude relationship, when it only affects the field direction. The strategy is to use the absolute value of charge when calculating field magnitude, then determine direction separately. - Two fixed source charges, +Q and −Q, are separated by a distance 2d. A test charge is placed at the midpoint between them. Which statement best describes the direction of the electric field at the midpoint?
Answer: It points from +Q toward −Q along the line joining them.
This question tests understanding of electric fields. The electric field is the vector sum of contributions from all source charges, with positive charges creating fields pointing away and negative charges creating fields pointing toward them. At the midpoint between +Q and -Q, the field from +Q points rightward (away from +Q) while the field from -Q also points rightward (toward -Q). Since both charges have equal magnitude and are equidistant, their fields have equal magnitude and same direction, resulting in a net field pointing from +Q toward -Q. Choice C incorrectly assumes opposite charges create canceling fields, confusing this with the zero field between identical charges. When analyzing fields from multiple charges, carefully determine each field's direction before adding vectors. - A fixed source charge −Q is at the origin. Point P is at y=0.25m on the +y axis. A small negative test charge −q is placed at P. Which statement best describes the direction of the electric field at P due to −Q?
Answer: It points in the −y direction.
Electric fields. Electric fields are properties of space created by source charges, with direction defined by the force on a positive test charge. A negative source charge at the origin creates a field pointing radially inward at all points, including point P on the +y axis. This means the field at P points toward the origin, which is in the -y direction, regardless of whether the actual test charge placed there is positive or negative. Choice C incorrectly assumes the field depends on the test charge's sign, confusing the field's existence with the force direction. Define electric field direction based on a positive test charge, then apply to any situation. - Two identical fixed source charges, each +Q, are separated by a distance 2d. A test charge is placed at the midpoint between them. Which statement best describes the electric field at the midpoint?
Answer: It is zero because the fields from the two charges cancel.
This question tests understanding of electric fields. The electric field at any point is the vector sum of fields from all source charges, following the principle of superposition. Each +Q charge creates a field pointing radially outward from itself, with magnitude E = kQ/d² at the midpoint. Since the charges are identical and equidistant from the midpoint, their field magnitudes are equal but directions are opposite (one points right, one points left). These equal and opposite vectors sum to zero at the midpoint. Choice D incorrectly assumes fields only exist where charges are located, misunderstanding that fields permeate all space. To find the net field, always add field vectors from each source charge, considering both magnitude and direction.
- A fixed source charge +2Q is at the origin. Point A is at distance r from the origin, and point B is at distance 2r. A small test charge is used only to measure the field. Compared to the electric field magnitude at B, the electric field magnitude at A is
Answer: four times as large.
This question tests understanding of electric fields. The electric field magnitude from a point charge follows E = kQ/r², showing an inverse square relationship with distance. Point A is at distance r while point B is at distance 2r from the source charge +2Q. The field at A is EA = k(2Q)/r², while at B it's EB = k(2Q)/(2r)² = k(2Q)/4r² = EA/4. Therefore, the field at A is four times as large as at B. Choice D incorrectly claims the fields are equal because the source charge is the same, ignoring how field strength decreases with distance. When comparing fields at different distances, always apply the 1/r² relationship to determine how the field changes with position.
- A fixed source charge +Q is at the origin. Point P is on the +x axis. A small test charge +q is placed at P to probe the field without changing it. Which statement best describes the direction of the electric field at P due to the source charge?
Answer: It points in the +x direction, away from the source charge.
This question tests understanding of electric fields. Electric fields are properties of space created by source charges, existing whether or not a test charge is present to detect them. A positive source charge +Q creates an electric field that points radially outward from the charge at all points in space. Since point P is on the +x axis (to the right of the origin), the field at P points in the +x direction, away from the positive source. Choice C incorrectly suggests the field direction depends on the test charge sign, confusing the field (which exists independently) with the force on a test charge (which does depend on the test charge's sign). To avoid this error, always determine the electric field first as a property of space due to source charges, then consider any forces on test charges placed in that field. - A fixed source charge +Q is at the origin. Point A is at r=0.20m and point B is at r=0.40m from the origin along the same radial line. A very small test charge is used to probe the field. Compared to the electric field strength at B, the electric field strength at A is
Answer: four times as large, because E∝1/r2.
Electric fields are properties of space whose strength depends on the source charge and distance from it. For a point charge, the electric field strength follows an inverse square law: E = kQ/r². Since point A is at half the distance from the source compared to point B (0.20 m vs 0.40 m), and E ∝ 1/r², the field at A is (0.40/0.20)² = 4 times stronger than at B. Choice A incorrectly inverts the relationship, suggesting E ∝ r² instead of E ∝ 1/r². The strategy is to remember that electric field strength decreases with the square of the distance from a point charge. - A fixed source charge +Q is at the origin. A small negative test charge −q is placed at point P on the +x axis to probe the field without changing the source. Which statement best describes the electric field at P due to the source charge?
Answer: It points in the +x direction, independent of the test charge sign.
This question tests understanding of electric fields. Electric fields are properties of space created by source charges, existing independently of any test charges used to detect them. A positive source charge +Q at the origin creates an electric field that points radially outward at all points, including point P on the +x axis. The field at P points in the +x direction regardless of whether a positive or negative test charge is placed there. Choice A incorrectly suggests the field direction depends on the test charge's sign, confusing the field itself with the force on the test charge (which would point opposite to the field for a negative charge). Always determine the electric field based solely on source charges before considering forces on test charges. - Two fixed source charges, +Q at x=−d and +4Q at x=+d, lie on the x axis. Point M is at x=0. A small positive test charge +q is placed at M to sense the field. Which statement best describes the direction of the net electric field at M due to the source charges?
Answer: It points in the −x direction because the +4Q field dominates at M.
This question tests understanding of electric fields. Electric fields from multiple sources superpose vectorially at each point. At the origin (M), the +Q charge at x = -d creates a field pointing in the +x direction (away from +Q), while the +4Q charge at x = +d creates a field pointing in the -x direction (also away from its position). The magnitudes are E₁ = kQ/d² and E₂ = k(4Q)/d² = 4kQ/d². Since E₂ > E₁ and points left, the net field points in the -x direction. Choice D incorrectly suggests the field depends on the test charge's mass, confusing field properties with particle dynamics. To find net fields, always calculate each field's magnitude and direction separately, then combine them vectorially. - A fixed source charge −6.0μC is located at x=+0.20m on the x axis. Point P is at the origin. A tiny positive test charge is placed at P to sample the field and does not alter the source. Which statement best describes the direction of the electric field at P due to the source charge?
Answer: It points in the +x direction, toward the negative source charge.
Electric fields are properties of space created by source charges, existing independently of any test charges. A negative source charge creates an electric field that points radially inward toward the charge at all surrounding points. Since point P (at the origin) is to the left of the negative source charge at x = +0.20 m, the field at P points toward the source, which is in the +x direction. Choice D incorrectly suggests the field direction depends on the test charge's sign, when in fact the field exists and has a definite direction regardless of any test charge. The strategy is to draw field lines pointing toward negative sources and away from positive sources. - Two fixed source charges lie on the x axis: +Q at x=−0.10m and −Q at x=+0.10m. Point P is at the origin. A tiny positive test charge is placed at P to probe the field. Which statement best describes the direction of the net electric field at P due to the source charges?
Answer: It points in the +x direction, from the positive source toward the negative source.
Electric fields are vector quantities that must be added using vector addition when multiple source charges are present. The positive charge at x = -0.10 m creates a field at the origin pointing in the +x direction (away from the positive charge), while the negative charge at x = +0.10 m also creates a field at the origin pointing in the +x direction (toward the negative charge). Since both individual fields point in the same direction (+x), they add constructively, giving a net field in the +x direction. Choice C incorrectly assumes equal magnitude charges always produce zero net field, ignoring that the charges have opposite signs. The strategy is to determine each field's direction separately, then add them as vectors. - A fixed source charge +Q is at the center of a hollow conducting spherical shell that is electrically neutral. Point P is located inside the cavity, at a distance r from the center (not touching the conductor). A very small positive test charge is used to probe the field. Which statement best describes the electric field at point P?
Answer: It is radially outward from the center.
Electric fields are properties of space created by source charges, and inside a conductor in electrostatic equilibrium, the field must be zero. However, point P is inside the cavity (not inside the conducting material), where the field from the central charge +Q exists unaffected by the conductor. The field at P points radially outward from the positive source charge at the center, following E = kQ/r². Choice B incorrectly applies the zero-field rule for inside conductors to the cavity region, which is not conducting material. The strategy is to distinguish between regions inside conducting material (E = 0) and cavities within conductors (E determined by charges in the cavity).
- A fixed source charge +2Q is at the origin. Point A is at r=0.30m and point B is at r=0.30m but in a different direction. A small test charge is placed at each point. Which statement best describes the electric field magnitudes EA and EB?
Answer: EA=EB because both points are the same distance from the source charge.
Electric fields. The electric field created by a point charge has spherical symmetry, meaning it depends only on the distance from the source charge, not on direction. Since both points A and B are at the same distance r = 0.30 m from the source charge, the electric field magnitude E = kQ/r² is identical at both locations. The field exists at these points as a property of space, regardless of whether test charges are placed there. Choice B incorrectly assumes the field varies with direction, confusing vector direction with magnitude. Remember that for a point charge, field magnitude depends only on radial distance. - A fixed source charge +Q is isolated in space. Points A and B are on the same radial line from +Q, with rB=2rA. A small test charge is used to sample the field. Compared to the electric field magnitude at A, the electric field magnitude at B is
Answer: one-fourth as large.
This question tests understanding of electric fields. The electric field created by a point charge decreases with the square of the distance from the source: E = kQ/r². Point B is twice as far from the source charge as point A (rB = 2rA), so the field at B is proportional to 1/(2rA)² = 1/4rA². This makes the field at B one-fourth as large as at A. Choice D incorrectly suggests the field is the same because the same test charge is used, confusing the field (which depends only on source charges and position) with measurements made by a test charge. To solve field problems correctly, always write the field equation E = kQ/r² first, focusing on how the field depends on distance from the source.
- A fixed source charge +Q is at the origin. Point P is on the +x axis at x=0.20m. A small positive test charge +q is placed at P. Which statement best describes the electric field at P due to +Q?
Answer: It points in the +x direction.
Electric fields. An electric field is a property of space created by source charges, existing whether or not a test charge is present. A positive source charge creates an electric field that points radially outward from the charge at all points in space. Since point P is on the +x axis to the right of the positive source charge at the origin, the electric field at P points away from the origin in the +x direction. Choice C incorrectly assumes the field depends on the test charge's sign, reflecting the misconception that electric fields only exist when forces are measured. Define the electric field as the force per unit positive test charge that would be experienced at that location. - A uniform electric field is produced in a region between large parallel plates (source charges on the plates). The field points to the right. A small negative test charge is placed at rest in the region without affecting the plates. Which statement best describes the direction of the electric field at the test charge's location?
Answer: It points right, set by the source charges on the plates.
Electric fields are properties of space created by source charges on the parallel plates, existing independently of any test charges. The uniform field between parallel plates points from positive to negative charges, which in this case is to the right as stated in the problem. This field direction is entirely determined by the configuration of charges on the plates and exists at every point in the region, including where the test charge is placed. Choice A incorrectly assumes the field direction depends on the sign of the test charge, confusing the field with the force on a charge. The strategy is to identify the electric field direction first, then use F = qE to find the force direction on any test charge.
