A circular region (radius R = 3.98 m) has a magnetic field perpendicular to the plane of the circle, with magnitude given by: B = 6.243 + 82.1t2 - 5.65, where B is in T and t is in seconds. At time t = 3.66 s, find the magnitude of the force, in N, felt by stationary charge q = 868 µC placed d = 7.4 m from the center of the circle (outside the circle). Give the answer as a positive if the force is to the right, and negative if the force is to the left.

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**Diagram 7: Magnetic Field and Charge Interaction**

This diagram illustrates the interaction of a point charge \( q \) within a magnetic field. The circular area represents a uniform magnetic field, with \( \textbf{X} \) symbols indicating that the magnetic field \( \mathbf{B} \) is directed into the page. A red circle represents the point charge \( q \) situated within this field.

Two vectors are shown:

- \( \mathbf{d} \) is a vector pointing upward from the center towards the charge \( q \).
- \( \mathbf{R} \) is a diagonal vector pointing downward to the right.

Key Points:

- The surrounding \( \textbf{X} \) symbols indicate the direction of the magnetic field being perpendicular to the plane of the page, specifically going inwards.
- The vector \( \mathbf{d} \) represents the distance from the center of the field to the charge.
- The vector \( \mathbf{R} \) may represent another relevant direction or force vector in the context of this diagram, hinting at the movement or force acting on the charge.

This diagram helps visualize the spatial relationship and interaction between the charge and the magnetic field in three dimensions.
Transcribed Image Text:**Diagram 7: Magnetic Field and Charge Interaction** This diagram illustrates the interaction of a point charge \( q \) within a magnetic field. The circular area represents a uniform magnetic field, with \( \textbf{X} \) symbols indicating that the magnetic field \( \mathbf{B} \) is directed into the page. A red circle represents the point charge \( q \) situated within this field. Two vectors are shown: - \( \mathbf{d} \) is a vector pointing upward from the center towards the charge \( q \). - \( \mathbf{R} \) is a diagonal vector pointing downward to the right. Key Points: - The surrounding \( \textbf{X} \) symbols indicate the direction of the magnetic field being perpendicular to the plane of the page, specifically going inwards. - The vector \( \mathbf{d} \) represents the distance from the center of the field to the charge. - The vector \( \mathbf{R} \) may represent another relevant direction or force vector in the context of this diagram, hinting at the movement or force acting on the charge. This diagram helps visualize the spatial relationship and interaction between the charge and the magnetic field in three dimensions.
Refer to diagram 7.  
A circular region (radius \( R = 3.98 \, \text{m} \)) has a magnetic field perpendicular to the plane of the circle, with magnitude given by:
\[ B = 6.24t^3 + 82.1t^2 - 5.65, \]
where \( B \) is in Teslas (T) and \( t \) is in seconds.

At time \( t = 3.66 \, \text{s} \), find the magnitude of the force, in Newtons (N), felt by a stationary charge \( q = 868 \, \mu\text{C} \) placed \( d = 7.4 \, \text{m} \) from the center of the circle (outside the circle). Give the answer as a positive if the force is to the right, and negative if the force is to the left.
Transcribed Image Text:Refer to diagram 7. A circular region (radius \( R = 3.98 \, \text{m} \)) has a magnetic field perpendicular to the plane of the circle, with magnitude given by: \[ B = 6.24t^3 + 82.1t^2 - 5.65, \] where \( B \) is in Teslas (T) and \( t \) is in seconds. At time \( t = 3.66 \, \text{s} \), find the magnitude of the force, in Newtons (N), felt by a stationary charge \( q = 868 \, \mu\text{C} \) placed \( d = 7.4 \, \text{m} \) from the center of the circle (outside the circle). Give the answer as a positive if the force is to the right, and negative if the force is to the left.
Expert Solution
Step 1

The expression for the magnetic force is as follows:

F=qv×B1

Here, F is the force, q is the charge, v is the velocity, B is the magnetic field.

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