Question

Electrons in a particle beam each have a kinetic energy of 4.0 × 10 −17 J. What is the magnitude of the electric field that will stop these electrons in a distance of 0.3 m? ( e = 1.6 × 10 −19 C)

Answer 1

Answer:

833N/C

Explanation:

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

Answer 2

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.