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MMLU-Pro / 9144 / A charge distribution that is spherically symmetric but not uniform radially…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E=Kr4E=K r^4, directed radially outward from the center of the sphere. Here rr is the radial distance from that center, and KK is a constant. What is the volume density ρ\rho of the charge distribution?
Plain-text mathematical notation (without MathML)
A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E=Kr⁴, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and K is a constant. What is the volume density ρ of the charge distribution?
Original LaTeX notation
A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude $E=K r^4$, directed radially outward from the center of the sphere. Here $r$ is the radial distance from that center, and $K$ is a constant. What is the volume density $\rho$ of the charge distribution?

category

physics

options

  1. $4$ $K \varepsilon_0 r^4$
  2. $2 K \varepsilon_0 r^5$
  3. $5 K \varepsilon_0 r$
  4. $7 K \varepsilon_0 r^3$
  5. $8 K \varepsilon_0 r^4$
  6. $4 K \varepsilon_0 r^3$
  7. $6$ $K \varepsilon_0 r^3$
  8. $3 K \varepsilon_0 r^2$
  9. $3$ $K \varepsilon_0 r^3$
  10. $6$ $K \varepsilon_0 r^2$

src

scibench-fund

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Source and history

upstream_id / Original problem ID
9144
task_id
ce1b7894-e22a-5025-a283-5621170f680c
task_key
default--test--9144
task_revision_id
1
config / split
default / test

Official source

initial import