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**Problem 3: Induced Current in a Rectangular Loop**

A rectangular loop (with sides \(a = 0.17 \, \text{m}\) and \(b = 0.34 \, \text{m}\)) is being pushed into a region where a uniform magnetic field is present. The loop moves with a speed of \(3.00 \, \text{m/s}\).

**Question:**

a) Calculate the induced current in the loop when the magnetic field has a uniform magnitude of \(7.50 \, \text{T}\) and the loop's resistance is \(65.0 \, \Omega\).

**Answer Box:**

\(\boxed{\phantom{0.00}} \, \text{Amp}\)

**Diagram Explanation:**

The diagram illustrates a rectangular loop entering a uniform magnetic field. 

- The magnetic field (\(\mathbf{B}\)) is directed into the page, indicated by the dots.
- The loop is represented by a blue rectangle.
- Side \(a\) is vertical, and side \(b\) is horizontal.
- The velocity (\(\mathbf{v}\)) of the loop's motion is shown by a red arrow pointing to the right, signifying the direction of the loop's movement into the magnetic field.

This setup describes a classic electromagnetic induction scenario, where the motion of the loop through the magnetic field induces an electromotive force (EMF), leading to a current when resistance is present.
Transcribed Image Text:**Problem 3: Induced Current in a Rectangular Loop** A rectangular loop (with sides \(a = 0.17 \, \text{m}\) and \(b = 0.34 \, \text{m}\)) is being pushed into a region where a uniform magnetic field is present. The loop moves with a speed of \(3.00 \, \text{m/s}\). **Question:** a) Calculate the induced current in the loop when the magnetic field has a uniform magnitude of \(7.50 \, \text{T}\) and the loop's resistance is \(65.0 \, \Omega\). **Answer Box:** \(\boxed{\phantom{0.00}} \, \text{Amp}\) **Diagram Explanation:** The diagram illustrates a rectangular loop entering a uniform magnetic field. - The magnetic field (\(\mathbf{B}\)) is directed into the page, indicated by the dots. - The loop is represented by a blue rectangle. - Side \(a\) is vertical, and side \(b\) is horizontal. - The velocity (\(\mathbf{v}\)) of the loop's motion is shown by a red arrow pointing to the right, signifying the direction of the loop's movement into the magnetic field. This setup describes a classic electromagnetic induction scenario, where the motion of the loop through the magnetic field induces an electromotive force (EMF), leading to a current when resistance is present.
**Question 4 (b):**

What is the direction of the induced current in the loop?

- ○ Counter-clockwise
- ○ Clockwise

*Note: This multiple-choice question is designed to test understanding of electromagnetic induction concepts, such as Faraday's Law, and the right-hand rule for determining the direction of induced current flow in a conductive loop.*
Transcribed Image Text:**Question 4 (b):** What is the direction of the induced current in the loop? - ○ Counter-clockwise - ○ Clockwise *Note: This multiple-choice question is designed to test understanding of electromagnetic induction concepts, such as Faraday's Law, and the right-hand rule for determining the direction of induced current flow in a conductive loop.*
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