GATE Engineering Sciences Practice Quiz

Question 1

Let φ(x,y,z) be a twice continuously differentiable scalar field. Which identity is always true?

Accepted Answer

∇×(∇φ)=0

Question 2

For a twice continuously differentiable vector field A(x,y,z), which identity is always valid?

Accepted Answer

∇·(∇×A)=0

Question 3

For a smooth scalar field φ, evaluate ∇·(∇×(∇φ)).

Accepted Answer

0

Question 4

Let A and B be smooth vector fields satisfying ∇·A=0 and ∇·B=0. Then ∇×(A×B) simplifies to

Accepted Answer

(B·∇)A−(A·∇)B

Question 5

For a differentiable scalar field φ and vector field A, which curl identity is correct?

Accepted Answer

∇×(φA)=φ(∇×A)+(∇φ)×A

GATE Engineering Sciences