Mathematical Physics-I MCQs

Direction of gradient can be calculated by the relation

• ∇φ.AA

• ∇φ∇φ

• grad φ1.grad φ2grad φ1grad φ2

• None of these

If ∇.A=0 then A is

• Solenoiadal field vector

• incompressible field vector

• there is no source and no sink

• All of these

If ∇×A=0 then A is

• Irrotational field vector

• conservative

• Energy is conserved in A

• All of these

Work, electric potential, vorticity and Ampere's law are examples of

• volume integral

• Surface integral

• line integral

• None of these

dS for yz-plane is calculated by the relation

• dxdyn.k

• dydzn.i

• dzdxn.j

• None of these

An integral used to compute the total value of a quantity (total charge, total mass etc) is

• line integral

• surface integral

• volume integral

• All of these

Line to surface integral inter conversion is

• Stoke's theorem

• Gauss Divergence theorem

• Green's theorem

• None of these

In spherical polar coordinates (r,θ,φ), φ varies

• 0 to 2π

• 0 to π

• 0 to π/2

• None of these

if ∭dxdydz is equal to

• area of circle

• area of surface

• volume of sphere

• None of these

Square of velocity in spherical polar coordinates is

• v2=x2+y2+z2

• v2=r2+r2θ2+r2sinθ2φ2

• v2=ρ2+ρ2φ2+z2

• None of these