Question

if r = xi + yj + zk then curl r =​

Answer 1

Given:

r = xi + yj + zk

To find:

Curl of r = xi + yj + zk

Solution:

curl r = ∇ × r

$curl \ r = \left[\begin{array}{ccc}i&j&k\\ \frac{\delta}{\delta x} &\frac{\delta}{\delta y}&\frac{\delta}{\delta z}\\r_1&r_2&r_3\end{array}\right]$

$curl \ r = (\frac{\delta r_3}{\delta y} - \frac{\delta r_2}{\delta z} )i + (\frac{\delta r_1}{\delta z} - \frac{\delta r_3}{\delta x} )j + (\frac{\delta r_3}{\delta x} - \frac{\delta r_1}{\delta y} )k$

Here,

r₁ = x

r₂ = y

r₃ = z

curl r = (0 - 0)i + (0 - 0)j + (0 - 0)k

curl r = 0

So, curl r = 0