Induced EMF: Find Flux for Rectangular Loop in z-y Plane

[robert25pl]

Can someone check my equation for flux. Thanks

A rectangular loop in the z-y plane is situated at t = 0 at the points (x=1,z=0), (x=1,z=5), (x=4,z=5), and (x=4,z=0). The rod of the loop with end points (x=4,z=0), and (x=4,z=5) is moving in the x-direction with a velocity
$$v=5\vec{i}$$m/s while the rest of the loop remains fixed. Find induced emf in the loop for all t

B = (10/x) cos100t j

$$\psi=\int_{s}B\cdot\,ds=\int_{xo=1}^{xo=4} \int_{z=0}^{5}\frac{10}{x}cos100t\vec{j}\cdot\, dx\,dz\vec{j}$$

 

[OlderDan]

Can someone check my equation for flux. Thanks

A rectangular loop in the z-y plane is situated at t = 0 at the points (x=1,z=0), (x=1,z=5), (x=4,z=5), and (x=4,z=0). The rod of the loop with end points (x=4,z=0), and (x=4,z=5) is moving in the x-direction with a velocity
$$v=5\vec{i}$$m/s while the rest of the loop remains fixed. Find induced emf in the loop for all t

B = (10/x) cos100t j

$$\psi=\int_{s}B\cdot\,ds=\int_{x=0}^{xo+5t} \int_{z=0}^{5}\frac{10}{x}cos100t\vec{j}\cdot\, dx\,dz\vec{j}$$

Looks OK to me except the lower limit on the x integral should be 1, not zero, with xo = 4 in the upper limit. I assume you can simplify and integrate this.

 

[robert25pl]

Yes I can do that and then find emf.

 

[robert25pl]

$$\psi=\int_{s}B\cdot\,ds=\int_{x=1}^{4+5t} \int_{z=0}^{5}\frac{10}{x}cos100t\vec{j}\cdot\, dx\,dz\vec{j}$$