Refer to diagram 3. A closed circular loop (N = 555 turns, radius r= 5.54 cm, resistance R = 6.32 2) sits in a magnetic field B pointing perpendicular to the plane of the loop and into the page. The magnitude of the magnetic field changes with time according to: 3 = 3.75t2 + 5.44t + 97.9, where B is in T and t is in seconds. After 0.578 seconds, find I, the current induced in the loop, in A. Give the answer as positive if the current runs clockwise in the loop, and negative if the current runs counter-clockwise.

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**Diagram 3 Explanation**

The diagram consists of a series of "X" marks arranged in the formation of a 3x3 grid. In the center of the grid is a circle enclosing a single "X". Here's a detailed breakdown:

- **Outer Arrangement**: There are "X" marks occupying each position in a grid format:
  - The top row contains three X's.
  - The middle row contains two X's on the sides with a circle in the middle.
  - The bottom row also contains three X's.

- **Central Circle**: The circle is drawn in the middle of the diagram, enclosing the central "X" mark, indicating a point of emphasis or differentiation from the surrounding "X" marks.

This layout may be used to illustrate concepts such as centrality, focus, or grouping in an educational context.
Transcribed Image Text:**Diagram 3 Explanation** The diagram consists of a series of "X" marks arranged in the formation of a 3x3 grid. In the center of the grid is a circle enclosing a single "X". Here's a detailed breakdown: - **Outer Arrangement**: There are "X" marks occupying each position in a grid format: - The top row contains three X's. - The middle row contains two X's on the sides with a circle in the middle. - The bottom row also contains three X's. - **Central Circle**: The circle is drawn in the middle of the diagram, enclosing the central "X" mark, indicating a point of emphasis or differentiation from the surrounding "X" marks. This layout may be used to illustrate concepts such as centrality, focus, or grouping in an educational context.
Refer to diagram 3.

A closed circular loop (\(N = 555\) turns, radius \(r = 5.54 \, \text{cm}\), resistance \(R = 6.32 \, \Omega\)) sits in a magnetic field \(B\) pointing perpendicular to the plane of the loop and into the page. The magnitude of the magnetic field changes with time according to:

\[ B = 3.75t^2 + 5.44t + 97.9, \]

where \(B\) is in Tesla (T) and \(t\) is in seconds.

After 0.578 seconds, find \(I\), the current induced in the loop, in amperes (A). Give the answer as positive if the current runs clockwise in the loop, and negative if the current runs counter-clockwise.
Transcribed Image Text:Refer to diagram 3. A closed circular loop (\(N = 555\) turns, radius \(r = 5.54 \, \text{cm}\), resistance \(R = 6.32 \, \Omega\)) sits in a magnetic field \(B\) pointing perpendicular to the plane of the loop and into the page. The magnitude of the magnetic field changes with time according to: \[ B = 3.75t^2 + 5.44t + 97.9, \] where \(B\) is in Tesla (T) and \(t\) is in seconds. After 0.578 seconds, find \(I\), the current induced in the loop, in amperes (A). Give the answer as positive if the current runs clockwise in the loop, and negative if the current runs counter-clockwise.
Expert Solution
Step 1

From figure we can see the magnetic field is directed downward and from the given equation for magnetic field we can see it is increasing with time. Therefore magnetic flux passes through the loop also increases with time. Therefore the direction of induced current will be in such a way so that magnetic field due to this current must be opposite to the direction of applied magnetic field, and this is possible only if direction of induced current counter-clockwise.

Therefore induced current is directed in counter-clockwise direction.

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