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AP · AP 2 · free response

AP Physics 2: Algebra-Based · Question 8

AP Physics 2: Algebra-Based · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
12
Topics
1
Answer
Complete
Point charges +2q and −q fixed a distance d apart on a horizontal line++2q−qorigind
Figure 4Two point charges rest on a long horizontal dashed line that extends well beyond both of them. On the left, at a point labelled "origin", is a circle containing a plus sign, labelled +2q. A distance to the right of it is a circle containing a minus sign, labelled −q, and that separation is marked d by a dimension line drawn between the two centres below the charges. Nothing else is marked anywhere on the line, in either direction.
free response12 marks

Two point charges are fixed on a horizontal line: a charge +2q at the origin, and a charge −q at a distance d to the right of it.

  1. (a)

    Sketch Sketch the electric field lines in the region around the two charges. Indicate the direction of each line with an arrow.

    3 marks
  2. (b)

    Determine Determine the location on the line through the two charges at which the net electric field is zero. Indicate whether it lies to the left of +2q, between the charges, or to the right of −q, and justify that region before calculating.

    4 marks
  3. (c)

    Determine Determine whether there is a point on the line between the two charges at which the electric potential is zero, and if so, where.

    3 marks
  4. (d)

    Explain Explain why the point where the field is zero and the point where the potential is zero are in different places.

    2 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: 1 point: lines begin on the positive charge and end on the negative charge, with arrows pointing away from +2q and towards −q 1 point: twice as many lines leave +2q as arrive at −q, with the surplus continuing outward to large distances 1 point: lines meet both charges radially and never cross one another
01

(a)

3 marks

Sketch Sketch the electric field lines in the region around the two charges. Indicate the direction of each line with an arrow.

How to approach it

Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.

  1. 1

    1 point: lines begin on the positive charge and end on the negative charge, with arrows pointing away from +2q and towards −q

  2. 2

    1 point: twice as many lines leave +2q as arrive at −q, with the surplus continuing outward to large distances

  3. 3

    1 point: lines meet both charges radially and never cross one another

02

(b)

4 marks

Determine Determine the location on the line through the two charges at which the net electric field is zero. Indicate whether it lies to the left of +2q, between the charges, or to the right of −q, and justify that region before calculating.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    1 point: the null point must lie beyond the smaller charge, to the right of −q, because only there do the two fields oppose and the weaker charge is closer

  2. 2

    1 point: sets k(2q)/(d + x)² = kq/x², where x is measured from −q

  3. 3

    1 point: 2x² = (d + x)², so x√2 = d + x

  4. 4

    1 point: x = d/(√2 − 1) = 2.4d to the right of −q

03

(c)

3 marks

Determine Determine whether there is a point on the line between the two charges at which the electric potential is zero, and if so, where.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    1 point: potentials are scalars, so a zero requires k(2q)/r₁ = kq/r₂ with r₁ + r₂ = d

  2. 2

    1 point: 2r₂ = r₁, so r₂ = d/3

  3. 3

    1 point: the potential is zero at a distance d/3 to the left of −q (that is, 2d/3 from +2q)

04

(d)

2 marks

Explain Explain why the point where the field is zero and the point where the potential is zero are in different places.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    1 point: the field is a vector sum, so it vanishes where two contributions are equal in magnitude and opposite in direction — which can only happen outside the pair

  2. 2

    1 point: the potential is a scalar sum, so it vanishes where two contributions of opposite sign are equal in magnitude, which happens between the charges; the two conditions are different, so the points differ

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