# Solved Problems-7

Problem-7

(a) Determine the constant

(b) Find the value of the constant

(c) Find the constants

*c*such that the vector will be solenoidal.(b) Find the value of the constant

*Q*to make , solenoidal.(c) Find the constants

*a, b, c*so that the vector, is irrotational.Solution

(a)

The vector will be solenoidal if its divergence is zero.

(b)

The vector will be solenoidal if its divergence is zero.

(c)

The vector will be irrotational if its curl is zero.

This vector will be zero if and only if its components are individually zero.

and

Hence,

The vector will be solenoidal if its divergence is zero.

(b)

The vector will be solenoidal if its divergence is zero.

(c)

The vector will be irrotational if its curl is zero.

This vector will be zero if and only if its components are individually zero.

and

Hence,

*a*= 4,*b*= 2,*c*= -1.