long solenoid with 13.1 turns/cm and a radius of 10.2 cm carries a current of 29.9 mA. A cu onductor located along the central axis of the solenoid. (a) At what radial distance from the f the resulting magnetic field be at 50.3° to the axial direction? (b) What is the magnitude of

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Chapter1: Units, Trigonometry. And Vectors
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For the first image asking for what is the magnetic field of a b and c Just answer part c which is one question while for image 2 answer all. Thanks
### Magnetic Field in a Solenoid and a Straight Conductor

**Problem Statement:**
A long solenoid with 13.1 turns/cm and a radius of 10.2 cm carries a current of 29.9 mA. A current of 15.3 A exists in a straight conductor located along the central axis of the solenoid.

**Questions:**
(a) At what radial distance from the axis in centimeters will the direction of the resulting magnetic field be at 50.3° to the axial direction?

(b) What is the magnitude of the magnetic field there?

**Input Fields:**

- (a) 
  - Number: [Input Box]
  - Units: [Dropdown Menu for Units]
  
- (b) 
  - Number: [Input Box]
  - Units: [Dropdown Menu for Units]

This exercise is designed to enhance understanding of magnetic fields in solenoids and conductors. Calculations may include using formulas for magnetic fields within solenoids and the superposition principle to calculate the resultant magnetic field direction and magnitude.
Transcribed Image Text:### Magnetic Field in a Solenoid and a Straight Conductor **Problem Statement:** A long solenoid with 13.1 turns/cm and a radius of 10.2 cm carries a current of 29.9 mA. A current of 15.3 A exists in a straight conductor located along the central axis of the solenoid. **Questions:** (a) At what radial distance from the axis in centimeters will the direction of the resulting magnetic field be at 50.3° to the axial direction? (b) What is the magnitude of the magnetic field there? **Input Fields:** - (a) - Number: [Input Box] - Units: [Dropdown Menu for Units] - (b) - Number: [Input Box] - Units: [Dropdown Menu for Units] This exercise is designed to enhance understanding of magnetic fields in solenoids and conductors. Calculations may include using formulas for magnetic fields within solenoids and the superposition principle to calculate the resultant magnetic field direction and magnitude.
**Educational Website Content:**

**Magnetic Field Components at Point P**

**Problem Statement:**
Determine the components of the magnetic field \((a) B_x\), \((b) B_y\), \((c) B_z\) at point P in the figure if \(I = 40 \, \text{A}\) and \(a = 8.4 \, \text{cm}\). Note that the wires are not long.

**Diagram Explanation:**
The diagram features a square loop with sides labeled \(a\). There is a point P located inside the square at a position \(a/4\) from both the top and left sides of the square. The current, \(I\), flows around the loop in a counterclockwise direction.

**Calculation Inputs:**

- \((a) B_x\): Enter a number and choose the units (default is mT).
- \((b) B_y\): Enter a number and choose the units (default is mT).
- \((c) B_z\): Enter a number and choose the units (default is mT).

Please input the calculated values to determine the magnetic field components at point P.
Transcribed Image Text:**Educational Website Content:** **Magnetic Field Components at Point P** **Problem Statement:** Determine the components of the magnetic field \((a) B_x\), \((b) B_y\), \((c) B_z\) at point P in the figure if \(I = 40 \, \text{A}\) and \(a = 8.4 \, \text{cm}\). Note that the wires are not long. **Diagram Explanation:** The diagram features a square loop with sides labeled \(a\). There is a point P located inside the square at a position \(a/4\) from both the top and left sides of the square. The current, \(I\), flows around the loop in a counterclockwise direction. **Calculation Inputs:** - \((a) B_x\): Enter a number and choose the units (default is mT). - \((b) B_y\): Enter a number and choose the units (default is mT). - \((c) B_z\): Enter a number and choose the units (default is mT). Please input the calculated values to determine the magnetic field components at point P.
Expert Solution
Step 1

Given:-

A long solenoid with  13.1 turns/cm and the radius of the solenoid r = 10.2 cm 

A solenoid carries a current I = 29.9 mA '

The current in the straight conductor is located along the central axis of the solenoid. 

Find:-

a)  At what radial distance from the axis will the direction of the resulting magnetic field be at 50.3° to the axial direction?

b)  what is the magnitude of the magnetic field is there?

 

 

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