Question

A rectangular loop of wire, with sides a, b, lies in the first quadrant of the xy plane, with one corner at the origin as shown in figure. y a b x In this region there is a nonuniform time-dependent magnetic field B(x, y, t) = 8 C x y^3 t^2 k (where C is a constant). a) Find the magnetic flux over the loop area b) Find the magnitude of the induced emf in the loop.

          A rectangular loop of wire, with sides a, b, lies in the first quadrant of the xy plane, with one corner at the origin as shown in figure.
y
a
b
x
In this region there is a nonuniform time-dependent magnetic field
B(x, y, t) = 8 C x y^3 t^2 k
(where C is a constant).
a) Find the magnetic flux over the loop area
b) Find the magnitude of the induced emf in the loop.

A rectangular loop of wire, with sides a, b, lies in the first quadrant of the xy plane, with one corner at the origin as shown in figure.
y
a
b
x
In this region there is a nonuniform time-dependent magnetic field
B(x, y, t) = 8 C x y^3 t^2 k
(where C is a constant).
a) Find the magnetic flux over the loop area
b) Find the magnitude of the induced emf in the loop.

Added by Rhonda B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Maitreya E

05/27/2022

Step 1

Given magnetic field \( B(x, y, t) = 8\epsilon xy^3t^2 \hat{k} \) and loop area \( A = ab \hat{k} \), the magnetic flux \( \Phi_B \) is given by: \[ \Phi_B = \int \int_S \vec{B} \cdot d\vec{A} \] \[ \Phi_B = \int \int_S 8\epsilon xy^3t^2 \hat{k} \cdot ab \hat{k} Show more…

Show all steps

Thanks for your feedback!

A rectangular loop of wire, with sides a, b, lies in the first quadrant of the xy plane, with one corner at the origin as shown in figure. In this region there is a nonuniform time-dependent magnetic field B(x, y, t) = 8 C x y^3 t^2 k (where C is a constant). a) Find the magnetic flux over the loop area b) Find the magnitude of the induced emf in the loop.