Where the question says "the four different positions", it's talking about
the four situations that are shown in the picture right next to the question.
The question can't be answered without seeing the picture.
Explanation:
- vector r lies on z- axis
- J is tilted at angle Ψ
- Orient x-axis such that w lies in x-z plane
Given:
Vector potential
Where, K = б*v ; r* = sqrt (R^2 + r^2 -2R*r*cos(θ')) ; da' = R^2*sin(θ')*dθ'dΦ'
Solution:
- Velocity of v point a point r' in a rotating rigid body is given by:
v = w x r' =
- where a = Ψ and b' = θ' and c' = Φ'
v = R*w [-(cos Ψ *sin θ' *sin Φ') x + (cos Ψ *sin θ' *cos Φ' - sin Ψ * cos θ') y
+ (cos Ψ *sin θ' *sin Φ') z ]
- Notice that terms like sin Φ' and cos Φ' contribute to zero:
- Hence,
- Evaluate integral u = cos (b')
- From we can determine two cases when r > R and r < R
Hence,
r < R
r > R
- Reverting back to original coordinate system given in figure 5.45:
r < R
r > R
Where, b = θ and c = direction along Φ.
Hence, A ( r , θ , Φ )
Pretty sure it's C - The Earth is rotating from East to West. It's the only answer that really makes sense.
I believe the correct answer is the bottom one. Hope this helped!
-TTL