Solved

A Potential Function of a Vector Field F Is Given $\theta$

Question 27

Multiple Choice

A potential function of a vector field F is given by $A potential function of a vector field F is given by , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F. Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = . A) r sin(2 \theta ) + r cos(2 \theta ) B) r sin(2 \theta ) + r cos(2 \theta ) C) r sin(2 \theta ) - r cos(2 \theta ) D) r sin(2 \theta ) + r cos(2 \theta ) E) r sin(2 \theta ) - r cos(2 \theta )$ , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F.
Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = $A potential function of a vector field F is given by , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F. Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = . A) r sin(2 \theta ) + r cos(2 \theta ) B) r sin(2 \theta ) + r cos(2 \theta ) C) r sin(2 \theta ) - r cos(2 \theta ) D) r sin(2 \theta ) + r cos(2 \theta ) E) r sin(2 \theta ) - r cos(2 \theta )$ .

A) r sin(2 $\theta$ ) + r cos(2 $\theta$ )
B) r sin(2 $\theta$ ) $A potential function of a vector field F is given by , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F. Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = . A) r sin(2 \theta ) + r cos(2 \theta ) B) r sin(2 \theta ) + r cos(2 \theta ) C) r sin(2 \theta ) - r cos(2 \theta ) D) r sin(2 \theta ) + r cos(2 \theta ) E) r sin(2 \theta ) - r cos(2 \theta )$ + r cos(2 $\theta$ ) $A potential function of a vector field F is given by , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F. Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = . A) r sin(2 \theta ) + r cos(2 \theta ) B) r sin(2 \theta ) + r cos(2 \theta ) C) r sin(2 \theta ) - r cos(2 \theta ) D) r sin(2 \theta ) + r cos(2 \theta ) E) r sin(2 \theta ) - r cos(2 \theta )$
C) r sin(2 $\theta$ ) $A potential function of a vector field F is given by , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F. Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = . A) r sin(2 \theta ) + r cos(2 \theta ) B) r sin(2 \theta ) + r cos(2 \theta ) C) r sin(2 \theta ) - r cos(2 \theta ) D) r sin(2 \theta ) + r cos(2 \theta ) E) r sin(2 \theta ) - r cos(2 \theta )$ - r cos(2 $\theta$ ) $A potential function of a vector field F is given by , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F. Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = . A) r sin(2 \theta ) + r cos(2 \theta ) B) r sin(2 \theta ) + r cos(2 \theta ) C) r sin(2 \theta ) - r cos(2 \theta ) D) r sin(2 \theta ) + r cos(2 \theta ) E) r sin(2 \theta ) - r cos(2 \theta )$
D) r sin(2 $\theta$ ) $A potential function of a vector field F is given by , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F. Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = . A) r sin(2 \theta ) + r cos(2 \theta ) B) r sin(2 \theta ) + r cos(2 \theta ) C) r sin(2 \theta ) - r cos(2 \theta ) D) r sin(2 \theta ) + r cos(2 \theta ) E) r sin(2 \theta ) - r cos(2 \theta )$ + $A potential function of a vector field F is given by , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F. Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = . A) r sin(2 \theta ) + r cos(2 \theta ) B) r sin(2 \theta ) + r cos(2 \theta ) C) r sin(2 \theta ) - r cos(2 \theta ) D) r sin(2 \theta ) + r cos(2 \theta ) E) r sin(2 \theta ) - r cos(2 \theta )$ r cos(2 $\theta$ ) $A potential function of a vector field F is given by , where (r , θ) are the polar coordinates and C is an arbitrary constant. Find F. Hint: The gradient of g(r , θ) is given by ∇g(r , θ) = . A) r sin(2 \theta ) + r cos(2 \theta ) B) r sin(2 \theta ) + r cos(2 \theta ) C) r sin(2 \theta ) - r cos(2 \theta ) D) r sin(2 \theta ) + r cos(2 \theta ) E) r sin(2 \theta ) - r cos(2 \theta )$
E) r sin(2 $\theta$ ) - r cos(2 $\theta$ )