Divergence & Curl Quizzes, Questions & Answers

Top Trending Divergence & Curl Quizzes

Divergence & Curl: Computing Operators for Common 2D & 3D Vector Fields

Divergence and curl are central tools in vector calculus, revealing how vector fields behave in physical and mathematical systems. Divergence measures how much a field spreads outward from a point, identifying sources and sinks...

Questions: 15 | Attempts: 13 | Last updated: Dec 16, 2025

Sample Question 1
Let F = < 3x, 5y, -2z > be a vector field representing the velocity of a fluid. Calculate the divergence of F.

6

< 3, 5, -2 >

0

10

Sample Question 2
Which of the following correctly classifies the output of the divergence and curl operators applied to a vector field F in 3D?

Divergence results in a vector; Curl results in a scalar.

Divergence results in a scalar; Curl results in a vector.

Both result in scalars.

Both result in vectors.

Divergence & Curl: Conservative, Solenoidal & Irrotational Vector Fields

Divergence and curl are powerful tools in vector calculus that reveal how vector fields behave in space. Divergence measures the net flux emerging from a point, helping identify sources, sinks, or incompressible behavior. Curl,...

Questions: 15 | Attempts: 11 | Last updated: Dec 16, 2025

Sample Question 1
Which of the following is the correct formula for the divergence of a vector field F = <P, Q, R> in R³?

(∂R/∂y - ∂Q/∂z) i + (∂P/∂z - ∂R/∂x) j + (∂Q/∂x - ∂P/∂y) k

∂P/∂x + ∂Q/∂y + ∂R/∂z

∂P/∂x + ∂Q/∂y - ∂R/∂z

∇ × F

Sample Question 2
Using the Del (nabla) operator ∇, how is the curl of a vector field F represented symbolically?

∇ · F

∇ × F

∇² F

∇ / F

Recent Divergence & Curl Quizzes

Divergence & Curl: Vector Identities, Product Rules & Physical Applications

Divergence and curl are essential concepts in vector calculus, describing how vector fields expand, compress, and rotate in space. Divergence measures the net outflow from a point, identifying sources, sinks, or incompressible...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
Compute the curl of F(x,y,z) = <3x, 4y, 5z>.

<0, 0, 0>

<5, 4, 3>

<0, 0, 12>

<4, -3, 0>

Divergence & Curl: Fluid Flow, Sources, Sinks & Rotational Motion

Divergence and curl are fundamental tools in vector calculus, used to describe how vector fields behave in space. Divergence measures how much a field spreads outward from a point, indicating sources or sinks, while curl measures...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
Using the Del (nabla) operator ∇ = < ∂/∂x, ∂/∂y, ∂/∂z >, how is the divergence of a vector field F represented symbolically?

∇ × F

∇ · F

∇ F

|∇ F|

Divergence & Curl: Core Definitions, Notation & Geometric Insight

Divergence and curl are two of the most fundamental operators in vector calculus, revealing how vector fields behave in space. Divergence measures how much a field spreads out from—or converges into—a point,...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
What is the divergence of a vector field F = P i + Q j + R k in three dimensions?

∂P/∂x + ∂Q/∂y + ∂R/∂z

∂R/∂y - ∂Q/∂z, ∂P/∂z - ∂R/∂x, ∂Q/∂x - ∂P/∂y

∂P/∂y + ∂Q/∂z + ∂R/∂x

∂P/∂z + ∂Q/∂x + ∂R/∂y