4. A square coil of silver wire of side length 20 cm with 500 turns is in a uniform magnetic field whose magnitude is increasing at a rate of 0.25 T/s, as shown in the figure below. X X X X X X X X X X X X Is there an induced current in this coil? If so, in which direction does the current flow? Explain your answers. (b) What is the EMF induced in the coil?
4. A square coil of silver wire of side length 20 cm with 500 turns is in a uniform magnetic field whose magnitude is increasing at a rate of 0.25 T/s, as shown in the figure below. X X X X X X X X X X X X Is there an induced current in this coil? If so, in which direction does the current flow? Explain your answers. (b) What is the EMF induced in the coil?
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c. What is the resistance of the coil given that the diameter of the wire is 2.00 mm? (Recall, resistance of wire is given by R = ρL/A, where ρ is the resistivity of the metal, L is the length of the wire, and A is the cross-sectional area.)
The figure shows a square coil with a series of "X" marks, indicating the direction of the magnetic field going into the page.
**(a)** Is there an induced current in this coil? If so, in which direction does the current flow? Explain your answers.
**(b)** What is the EMF induced in the coil?
#### Explanation
**(a) Induced Current in the Coil**
- **Presence of Induced Current:**
According to Faraday's Law of Electromagnetic Induction, an electromotive force (EMF) is induced in a coil when the magnetic flux through the coil changes over time. In this scenario, the magnetic field's magnitude is increasing, thereby changing the magnetic flux through the coil.
As the magnetic field increases at a rate of 0.25 T/s, there will be a change in the magnetic flux through the coil. Consequently, an EMF is induced, which drives a current through the coil.
- **Direction of Current Flow:**
The direction of the current flow can be determined using Lenz's Law, which states that the direction of the induced current will oppose the change in magnetic flux.
Here, the magnetic flux through the coil is increasing into the page. To oppose this increase, the induced current will generate its own magnetic field out of the page. Using the right-hand rule, for the induced magnetic field to point out of the page, the current must flow counterclockwise when viewed from above.
**(b) Calculation of Induced EMF**
Using Faraday's Law of Induction:
\[ \text{EMF} = -N \frac{d\Phi_B}{dt} \]
Where:
- \(N = 500\) (number of turns)
- \(\frac{d\Phi_B}{dt}\) is the rate of change of magnetic flux through one loop of the coil.
Magnetic flux (\(\Phi_B\)) is given by:
\[ \Phi_B = B \cdot A \]
where](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F859743d5-9578-4a68-94b4-09f68a5c3500%2Fd9eb1f3d-b2a9-4cbd-a670-7d8b048854d3%2F205ezqu_processed.png&w=3840&q=75)
Transcribed Image Text:### Induced Current and Electromotive Force (EMF) in a Silver Coil
#### Problem Statement
A square coil of silver wire with a side length of 20 cm and 500 turns is placed in a uniform magnetic field. The magnitude of the magnetic field is increasing at a rate of 0.25 T/s, as shown in the figure below.
The figure shows a square coil with a series of "X" marks, indicating the direction of the magnetic field going into the page.
**(a)** Is there an induced current in this coil? If so, in which direction does the current flow? Explain your answers.
**(b)** What is the EMF induced in the coil?
#### Explanation
**(a) Induced Current in the Coil**
- **Presence of Induced Current:**
According to Faraday's Law of Electromagnetic Induction, an electromotive force (EMF) is induced in a coil when the magnetic flux through the coil changes over time. In this scenario, the magnetic field's magnitude is increasing, thereby changing the magnetic flux through the coil.
As the magnetic field increases at a rate of 0.25 T/s, there will be a change in the magnetic flux through the coil. Consequently, an EMF is induced, which drives a current through the coil.
- **Direction of Current Flow:**
The direction of the current flow can be determined using Lenz's Law, which states that the direction of the induced current will oppose the change in magnetic flux.
Here, the magnetic flux through the coil is increasing into the page. To oppose this increase, the induced current will generate its own magnetic field out of the page. Using the right-hand rule, for the induced magnetic field to point out of the page, the current must flow counterclockwise when viewed from above.
**(b) Calculation of Induced EMF**
Using Faraday's Law of Induction:
\[ \text{EMF} = -N \frac{d\Phi_B}{dt} \]
Where:
- \(N = 500\) (number of turns)
- \(\frac{d\Phi_B}{dt}\) is the rate of change of magnetic flux through one loop of the coil.
Magnetic flux (\(\Phi_B\)) is given by:
\[ \Phi_B = B \cdot A \]
where
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