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Physics 5C: Electricity, Magnetism, and Modern Physics SPRING 2026 University of California

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The two source charges (−Q at y = 0 and +9Q at y = d) remain fixed in place for the rest of this problem. Use the expression for V (y) given on the first page of this problem, which gives the potential due to these two charges only. (10d) (3 points) Calculate V at y1 = 2d and y2 = 3d. Show your work below, then record your answers. Solution: V (2d) = − kQ 2d + 9kQ 2d − d = − kQ 2d + 9kQ d = + 17kQ 2d = +7.6 × 105 V V (3d) = − kQ 3d + 9kQ 3d − d = − kQ 3d + 9kQ 2d = + 25kQ 6d = +3.7 × 105 V i. V (y1) = ii. V (y2) = iii. Which is larger?

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Institution
Physics 5C
Course
Physics 5C

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Physics 5C – E&M and Modern Physics
Exam 1 – Spring 2026 Version B

Physics 5C: Electricity, Magnetism, and Modern
Physics
Exam 1 – Spring 2026
Version B




Name:


UID:




ˆ Time limit: 75 minutes.

ˆ Closed book; no notes. Formula sheet provided on the next page.

ˆ Calculator allowed (scientific or graphing). No phones, smartwatches, or devices with com-
munication capabilities.

ˆ Express all numerical answers in SI units. Include units with your answers.

ˆ Directions may be expressed in words (e.g., “toward Q1 ,” “in the +x direction”) or using unit
vectors (x̂, ŷ). Either is acceptable.

ˆ Part I (Multiple Choice): Write the letter of your answer in the box provided.

ˆ Part II (Free Response): Show all work for full credit. Box your final numerical answers
with units.




Section Points Score
Part I: Multiple Choice (8 × 5) 40
Part II: Free Response 1 30
Part II: Free Response 2 30
Total 100




1

, Physics 5C Exam 1 – Spring 2026 Version B

Formula Sheet

Coulomb’s Law
|Q1 ||Q2 |
F =k , k = 8.99 × 109 N · m2 /C2
r2

Electric Field (point charge)
|Q|
E=k
r2

Force from Electric Field
F⃗ = q E



Electric Potential (point charge)

Q
V =k
r

Potential Energy (two point charges)

Q1 Q2
U =k
r

Potential Energy from Potential

U = qV


Superposition
⃗ net = E
E ⃗1 + E
⃗2 + · · · , Vnet = V1 + V2 + · · ·

Constants
e = 1.60 × 10−19 C, k = 8.99 × 109 N · m2 /C2

Mathematics
p opposite adjacent sin θ
c = a2 + b2 , sin θ = , cos θ = , tan θ =
hypotenuse hypotenuse cos θ


Metric Prefixes
µ = 10−6 , n = 10−9 , p = 10−12




2

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Institution
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Course
Physics 5C

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