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

• robert25pl
In summary, the conversation discusses a rectangular loop in the z-y plane with a moving rod in the x-direction and a fixed loop. The equation for induced emf is given by integrating the magnetic field with respect to path length. The lower limit on the x integral should be 1, not 0.
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

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

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robert25pl said:
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.

Yes I can do that and then find emf.

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

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1. What is induced EMF?

Induced EMF (electromotive force) is the voltage or potential difference that is generated in a conductor due to a change in magnetic flux through the conductor.

2. How is EMF induced in a rectangular loop in the z-y plane?

EMF is induced in a rectangular loop in the z-y plane when there is a changing magnetic field passing through the loop. This can be caused by either a varying magnetic field or by moving the loop through a stationary magnetic field.

3. What is the formula for calculating induced EMF in a rectangular loop in the z-y plane?

The formula for calculating induced EMF in a rectangular loop in the z-y plane is: E = -N * (dΦ/dt), where E is the induced EMF, N is the number of turns in the loop, and dΦ/dt is the rate of change of magnetic flux through the loop.

4. How does the orientation of the rectangular loop affect the induced EMF?

The orientation of the rectangular loop does not affect the induced EMF. As long as the loop is in the z-y plane, the induced EMF will be the same regardless of its orientation.

5. What is the significance of finding the flux in a rectangular loop in the z-y plane?

Finding the flux in a rectangular loop in the z-y plane allows us to determine the amount of induced EMF in the loop, which can then be used to calculate the current and other electrical properties of the loop. This is important in understanding and analyzing the behavior of electromagnetic systems.

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