To find the force on an electron moving in a magnetic field, we can use the formula for the magnetic force:
\[
F = q \cdot (v \times B)
\]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge of the electron,
- \( v \) is the velocity of the electron,
- \( B \) is the magnetic field strength,
- \( \times \) denotes the cross product.
### Step 1: Identify the values
- The charge of an electron, \( q = -1.6 \times 10^{-19} \) C (the negative sign indicates the charge is negative).
- The velocity of the electron, \( v = 15 \) m/s.
- The magnetic field strength, \( B = 5 \) T.
### Step 2: Calculate the magnitude of the force
Since the force is given by the cross product, we can simplify the calculation by considering the magnitude of the force:
\[
F = |q| \cdot v \cdot B \cdot \sin(\theta)
\]
where \( \theta \) is the angle between the velocity vector and the magnetic field vector. If we assume that the electron is moving perpendicular to the magnetic field (which gives the maximum force), then \( \sin(\theta) = 1\).
Thus, the formula simplifies to:
\[
F = |q| \cdot v \cdot B
\]
### Step 3: Substitute the values into the equation
Now, substituting the known values into the equation:
\[
F = (1.6 \times 10^{-19} \, \text{C}) \cdot (15 \, \text{m/s}) \cdot (5 \, \text{T})
\]
### Step 4: Perform the calculation
Calculating the force:
\[
F = 1.6 \times 10^{-19} \cdot 15 \cdot 5
\]
Calculating \( 15 \cdot 5 = 75 \):
\[
F = 1.6 \times 10^{-19} \cdot 75
\]
Now, calculating \( 1.6 \cdot 75 = 120 \):
\[
F = 120 \times 10^{-19} \, \text{N}
\]
This can be expressed in scientific notation:
\[
F = 1.2 \times 10^{-17} \, \text{N}
\]
### Final Answer
The force on the electron is \( 1.2 \times 10^{-17} \, \text{N} \).
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