The magnetic field B due to a small current loop (which is placed at the origin) is called a magnetic dipole. Letp = (x² + y² + z²)¹/² For p large, B = curl(A), whereA = (-33, -3,0)RCurrent loop(a) Let C be a horizontal circle of radius R with center (0, 0, c), and parameterization c(t) where c is large.Which of the following correctly explains why A is tangent to C?A(c(t)) =So, A(c(t)) =A(c(t))-(-²A(c(t)) ==A(c(t))cos(0,0)p3(1). Therefore, A is parallel to c'(t) and tangent to C.Rcos(t) R sin(t)= (-OSR sin(t) R cos(1)p³So, A(c(1)) = -c'(1). Therefore, A is parallel to c'(t) and tangent to C.OBdS ==and c'(t)= (-R sin(t), R cos(t), 0)Rin(1,0) and c'(t) = (R cos(1), -R sin(1), 0)So, A(c(t)) c(t) = 0. Therefore, A is perpendicular to c'(t) and tangent to C.OR sin(1) R cos(1)(R$ R COS(0,0) and c'(t) = (R cos(t), - R sin(t), 0)R cos(1)p3So, A(c(t)) - c'(t) = 0. Therefore, A is perpendicular to c' (t) and tangent to C.R sin(t)-and c'(t)= (-R sin(t), R cos(t), 0)(b) Suppose that R = 6 and c = 900. Use Stokes' Theorem to calculate the flux of B through C.(Use decimal notation. Round your answer to eight decimal places.)

Given Data: The value of Rho is..The magnetic vector potential, .The radius of the loop is To Find:…

The magnetic field B due to a small current loop (which is placed at the origin) is called a magnetic dipole. Let p = (x² + y² + z²)¹/² For p large, B = curl(A), where 1/2 ^-(-3-30) A = b (a) Let C be a horizontal circle of radius R with center (0, 0, c), and parameterization c(t) where c is large. Current loop Which of the following correctly explains why A is tangent to C? O S A(c(t)) = =(- A(c(t)) = So, A(c(t)) = c(1). Therefore, A is parallel to c'(1) and tangent to C. R cos(t) R sin(t) (- A(c(t)) = A(c(t)) (0,0) So, A(c(1)) = -c'(1). Therefore, A is parallel to c'(t) and tangent to C. R sin(t) R cos(1) (sin() cos(0,0) and c'(t) = (R cos(t), - R sin(t), 0) O . BdS = R sin(t) R cos(1) So, A(c(t)) c(t) = 0. Therefore, A is perpendicular to c'(t) and tangent to C. O R cos(1) R sin(t) and c'(t) = (-R sin(t), R cos(t), 0) So, A(c(t)) c'(t) = 0. Therefore, A is perpendicular to c'(t) and tangent to C. and c'(t) = (-R sin(t), R cos(t), 0) = Rin(0,0) and c'(t) = (R cos(1), - R sin(t), 0) (b) Suppose that R = 6 and c = 900. Use Stokes' Theorem to calculate the flux of B through C. (Use decimal notation. Round your answer to eight decimal places.)

The magnetic field B due to a small current loop (which is placed at the origin) is called a magnetic dipole. Let p = (x² + y² + z²)¹/² For p large, B = curl(A), where 1/2 ^-(-3-30) A = b (a) Let C be a horizontal circle of radius R with center (0, 0, c), and parameterization c(t) where c is large. Current loop Which of the following correctly explains why A is tangent to C? O S A(c(t)) = =(- A(c(t)) = So, A(c(t)) = c(1). Therefore, A is parallel to c'(1) and tangent to C. R cos(t) R sin(t) (- A(c(t)) = A(c(t)) (0,0) So, A(c(1)) = -c'(1). Therefore, A is parallel to c'(t) and tangent to C. R sin(t) R cos(1) (sin() cos(0,0) and c'(t) = (R cos(t), - R sin(t), 0) O . BdS = R sin(t) R cos(1) So, A(c(t)) c(t) = 0. Therefore, A is perpendicular to c'(t) and tangent to C. O R cos(1) R sin(t) and c'(t) = (-R sin(t), R cos(t), 0) So, A(c(t)) c'(t) = 0. Therefore, A is perpendicular to c'(t) and tangent to C. and c'(t) = (-R sin(t), R cos(t), 0) = Rin(0,0) and c'(t) = (R cos(1), - R sin(t), 0) (b) Suppose that R = 6 and c = 900. Use Stokes' Theorem to calculate the flux of B through C. (Use decimal notation. Round your answer to eight decimal places.)