Answer:
-833.3 N/C
Explanation:
Kinetic energy, K, in terms of electric field, E, is given as:
K = qEr
q = charge = e = 1.6 × 10⁻¹⁹C
E = Electric field
r = distance = 0.3m
The electric field can be gotten by making E subject of formula:
E = K/(qr)
The electeic field needed to stop the electrons must be equal in magnitude to the electric field carried by these electrons:
E = (4.0 × 10⁻¹⁷)/(-1.6 × 10⁻¹⁹ * 0.3)
E = -833.3 N/C
This is the electric field needed to stop the electrons.
The negative sign means that the electric field must be in a direction opposite to the motion of the electrons.
833N/C
The work done (W) in stopping these electrons is equal in magnitude to the kinetic energy (K.E) of the electrons. i.e
W = K.E ---------------(i)
Where;
The work done is also equal in magnitude to the product of the force (F) required to stop these electrons and the distance (r) covered in stopping them. i.e
W = F x r -----------------(ii)
Also, the force (F) required is the magnitude of the product of the charge (Q)on the electrons and the magnitude of the electric field (E). i.e
F = Q x E ------------------(iii)
Combining equations (i) and (ii) we have;
K.E = F x r ---------------------(iv)
Substituting equation(iii) into equation (iv) gives;
K.E = Q x E x r ------------------------(v)
From the question;
K.E = 4.0 x 10⁻¹⁷J
Q = 1.6 x 10⁻¹⁹ C
r = 0.3
Substitute these values into equation (v) to give;
4.0 x 10⁻¹⁷ = 1.6 x 10⁻¹⁹ x E x 0.3
4.0 x 10⁻¹⁷ = 0.48 x 10⁻¹⁹ x E
Solve for E;
E = 4.0 x 10⁻¹⁷ / (0.48 x 10⁻¹⁹)
E = 8.33 x 10² N / C
E = 833 N/C
Therefore, the electric field that will stop these electrons in a distance of 0.3m is 833N/C
