Unit 1-3

A scalar field is a function that assigns a ______ to every point in space.

• Vector

• Scalar value

• Direction

• Matrix

Which of the following is NOT a vector field?

• Electric field

• Velocity field

• Temperature distribution in a room

• Magnetic field

The gradient of a scalar field represents the direction of ______.

• Maximum decrease

• Maximum increase

• Zero change

• Uniform distribution

If the divergence of a vector field is zero, the field is said to be ______.

• Irrotational

• Solenoidal

• Conservative

• Isotropic

The gradient of a function is always ______.

• A scalar

• A vector

• A tensor

• Zero

Which mathematical operator is used to find the divergence of a vector field?

• ∇φ

• ∇⋅F

• ∇×F

• ∇²φ

The physical meaning of curl is related to ______.

• The rotational tendency of a field

• The divergence of a vector field

• The magnitude of a scalar field

• The uniformity of a function

A vector field with zero curl is called ______.

• Solenoidal

• Irrotational

• Conservative

• Both b and c

Gauss’s theorem relates the volume integral of divergence to the ______.

• Surface integral of the vector field

• Line integral of the vector field

• Scalar integral of the function

• Gradient of the function

Stokes' theorem relates the surface integral of the curl of a vector field to the ______.

• Volume integral

• Line integral

• Gradient integral

• None of the above