To determine the correct answer, let us go through the process of calculating the force acting on the electrons in a magnetic field. The formula for the magnetic force [tex]\( F \)[/tex] on a charged particle moving at a right angle to a magnetic field is given by:
[tex]\[ F = q \cdot v \cdot B \][/tex]
where:
- [tex]\( q \)[/tex] is the charge of the particle (in coulombs)
- [tex]\( v \)[/tex] is the velocity of the particle (in meters/second)
- [tex]\( B \)[/tex] is the magnetic field strength (in tesla)
Let's plug in the given values into the formula:
- Charge of the electron, [tex]\( q = 1.6 \times 10^{-19} \)[/tex] C
- Velocity of the electron, [tex]\( v = 6.5 \times 10^6 \)[/tex] m/s
- Magnetic field strength, [tex]\( B = 4.5 \times 10^2 \)[/tex] T
Substitute these values into the formula:
[tex]\[ F = (1.6 \times 10^{-19} \text{ C}) \times (6.5 \times 10^6 \text{ m/s}) \times (4.5 \times 10^2 \text{ T}) \][/tex]
When doing the multiplication, the result is:
[tex]\[ F = 4.68 \times 10^{-10} \text{ N} \][/tex]
Thus, the correct force acting on the electrons is [tex]\( 4.68 \times 10^{-10} \text{ N} \)[/tex].
Now let's match this result with the provided options:
A. [tex]\( 29 \times 10^6 1 H \)[/tex] - Incorrect and irrelevant dimensional unit
B. [tex]\( -39 \times 10^{-14} N \)[/tex] - Incorrect value and sign
C. [tex]\( 49 \times 49^{14} 4 \)[/tex] - Incorrect format and value
D. [tex]\( .65 \times 10^{-13} N \)[/tex] - Correctly formatted value close to [tex]\( 4.68 \times 10^{-10} \text{ N} \)[/tex]
Out of all the given options, none exactly match the result [tex]\( 4.68 \times 10^{-10} \text{ N} \)[/tex]. However, if we re-examine Option D in terms of scientific precision, [tex]\( 0.65 \times 10^{-13} N \)[/tex] can be reinterpreted as a formatting approximation:
[tex]\[ 0.65 \times 10^{-13} \text{ N} = 6.5 \times 10^{-14} \text{ N} \][/tex]
Since this does not correspond closely to [tex]\( 4.68 \times 10^{-10} \text{ N} \)[/tex], it appears none of the provided answers are correct. The correct force should be [tex]\( 4.68 \times 10^{-10} \text{ N} \)[/tex].
