The electrons in a particle beam each have a kinetic energy of 1.60×10−17 J. What are the magnitude and direction of the electric ﬁeld that will stop these electrons in a distance of 10.0cm?

Question

Elena Albarran · Accepted Answer

#E = F/q = 1.60×10^-16 N/1.60×10^-19 C = 1xx10^3 C#
Use the Work-Energy Theorem: #W_("net") = DeltaK# As the electron slows to a halt, its change in kinetic energy is: #DeltaK = K_f −K_i =0−(1.60×10^-17 J) = −1.60×10^-17 J # So #W = −1.60×10^-17 J # Let the electric force on the electron has magnitude #F#. The electron moves a distance #d = 10 .0 cm# opposite the direction of the force so that the work done is: #W =−Fd; −1.60×10^-17 J= −F(10.0×10^-2 m) # solving for, #F = 1.60×10^-16 N# Now knowing the charge of the electron we can evaluate the electric field, E: #E = F/q = 1.60×10^-16 N/1.60×10^-19 C = 1xx10^3 C#

Xavier Adame · Answer

undefined To find the magnitude and direction of the electric field that will stop the electrons in a distance of 10.0 cm, we can use the formula:

$$ K = q \cdot V $$

Where:
- $ K $ is the kinetic energy of the electron,
- $ q $ is the charge of the electron,
- $ V $ is the potential difference.

Given that the kinetic energy of each electron is $ 1.60 \times 10^{-17} $ J and the distance is 10.0 cm, we can calculate the potential difference using the formula:

$$ K = q \cdot V $$

$$ V = \frac{K}{q} $$

Given that the charge of an electron $ q $ is $ 1.6 \times 10^{-19} $ C, we can calculate $ V $.

$$ V = \frac{1.60 \times 10^{-17}}{1.6 \times 10^{-19}} $$

$$ V = 100 \, \text{V} $$

Now, to find the magnitude of the electric field ($ E $), we use the formula:

$$ E = \frac{V}{d} $$

Where $ d $ is the distance traveled by the electron.

$$ E = \frac{100}{0.1} $$

$$ E = 1000 \, \text{V/m} $$

The magnitude of the electric field required to stop the electrons in a distance of 10.0 cm is $ 1000 \, \text{V/m} $. Since the electric field is directed opposite to the direction of the electron's motion, its direction is opposite to the initial direction of the electron beam.