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The Gradient of a Scalar Field Expressed in Terms $\theta$

Question 19

Multiple Choice

The gradient of a scalar field $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ expressed in terms of polar coordinates [r, $\theta$ ] in the plane is $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ (r, $\theta$ ) = $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ + $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ . $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ Use the result above to find the necessary condition for the vector field F(r, $\theta$ ) = P(r, $\theta$ ) $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ + Q(r, $\theta$ ) $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ to be conservative.

A) $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ = $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$
B) $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ = r $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$
C) $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ = - $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$
D) $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ - r $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ = Q
E) $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ - $The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r$ = r