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MMLU-Pro / 9850 / A nonconducting spherical shell, with an inner radius of 4.0 mathrm{~cm} and…

Problem

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

question

A nonconducting spherical shell, with an inner radius of $4.0 \mathrm{~cm}$ and an outer radius of $6.0 \mathrm{~cm}$, has charge spread nonuniformly through its volume between its inner and outer surfaces. The volume charge density ρ\rho is the charge per unit volume, with the unit coulomb per cubic meter. For this shell ρ=b/r\rho=b / r, where rr is the distance in meters from the center of the shell and b=3.0μC/m2b=3.0 \mu \mathrm{C} / \mathrm{m}^2. What is the net charge in the shell?
Plain-text mathematical notation (without MathML)
A nonconducting spherical shell, with an inner radius of $4.0 \mathrm{~cm}$ and an outer radius of $6.0 \mathrm{~cm}$, has charge spread nonuniformly through its volume between its inner and outer surfaces. The volume charge density ρ is the charge per unit volume, with the unit coulomb per cubic meter. For this shell ρ=b/r, where r is the distance in meters from the center of the shell and b=3.0μC/m². What is the net charge in the shell?
Original LaTeX notation
A nonconducting spherical shell, with an inner radius of $4.0 \mathrm{~cm}$ and an outer radius of $6.0 \mathrm{~cm}$, has charge spread nonuniformly through its volume between its inner and outer surfaces. The volume charge density $\rho$ is the charge per unit volume, with the unit coulomb per cubic meter. For this shell $\rho=b / r$, where $r$ is the distance in meters from the center of the shell and $b=3.0 \mu \mathrm{C} / \mathrm{m}^2$. What is the net charge in the shell?

category

physics

options

  1. $1.5 \times 10^{-8} \mathrm{C}$
  2. $6.0 \times 10^{-8} \mathrm{C}$
  3. $4.6$ $10^{-8} \mathrm{C}$
  4. $4.0 \times 10^{-8} \mathrm{C}$
  5. $2.9$ $10^{-8} \mathrm{C}$
  6. $3.8$ $10^{-8} \mathrm{C}$
  7. $2.5 \times 10^{-8} \mathrm{C}$
  8. $7.2 \times 10^{-8} \mathrm{C}$
  9. $3.0 \times 10^{-8} \mathrm{C}$
  10. $5.2$ $10^{-8} \mathrm{C}$

src

scibench-fund

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Source and history

upstream_id / Original problem ID
9850
task_id
75e671fd-8c1d-5c0c-9ca7-74994686237d
task_key
default--test--9850
task_revision_id
1
config / split
default / test

Official source

initial import