A beam contains 7.8 x 106 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 7.3 x 105 m/s. What is (a) the magnitude of the current density and (b) direction of the current density J .(c) What additional quantity do you need to calculate the total current i in this ion beam? (a) Number i Units (b)
A beam contains 7.8 x 106 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 7.3 x 105 m/s. What is (a) the magnitude of the current density and (b) direction of the current density J .(c) What additional quantity do you need to calculate the total current i in this ion beam? (a) Number i Units (b)
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![### Problem Statement: Ion Beam Current Density Calculation
A beam contains \( 7.8 \times 10^6 \) doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of \( 7.3 \times 10^5 \) m/s.
#### Questions:
1. **(a)** What is the magnitude of the current density \( \mathbf{J} \)?
2. **(b)** What is the direction of the current density \( \mathbf{J} \)?
3. **(c)** What additional quantity do you need to calculate the total current \( I \) in this ion beam?
#### Inputs:
- **Ion Density**: \( 7.8 \times 10^6 \) ions/cm\(^3\)
- **Charge per Ion**: Doubly charged positive ions (each ion carries a charge of \( 2e \))
- **Ion Velocity**: \( 7.3 \times 10^5 \) m/s north
#### Outputs:
1. **(a)**
- **Number:**
\[ \boxed{} \]
- **Units:**
\[ \boxed{\text{}} \]
2. **(b)**
\[ \boxed{} \]
3. **(c)**
\[ \boxed{} \]
This problem requires calculating the current density in a beam of ions, determining its direction, and identifying additional quantities needed to compute the total current in the beam. The magnitude of current density \(\mathbf{J}\) can be derived from the product of the charge density and velocity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba35cc5f-959d-4f80-acdd-e9cc0bd31dfa%2Faed34a05-acc1-4749-ac6c-2e4d7e8f0eae%2F0a8mol_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement: Ion Beam Current Density Calculation
A beam contains \( 7.8 \times 10^6 \) doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of \( 7.3 \times 10^5 \) m/s.
#### Questions:
1. **(a)** What is the magnitude of the current density \( \mathbf{J} \)?
2. **(b)** What is the direction of the current density \( \mathbf{J} \)?
3. **(c)** What additional quantity do you need to calculate the total current \( I \) in this ion beam?
#### Inputs:
- **Ion Density**: \( 7.8 \times 10^6 \) ions/cm\(^3\)
- **Charge per Ion**: Doubly charged positive ions (each ion carries a charge of \( 2e \))
- **Ion Velocity**: \( 7.3 \times 10^5 \) m/s north
#### Outputs:
1. **(a)**
- **Number:**
\[ \boxed{} \]
- **Units:**
\[ \boxed{\text{}} \]
2. **(b)**
\[ \boxed{} \]
3. **(c)**
\[ \boxed{} \]
This problem requires calculating the current density in a beam of ions, determining its direction, and identifying additional quantities needed to compute the total current in the beam. The magnitude of current density \(\mathbf{J}\) can be derived from the product of the charge density and velocity.
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