Answer to Question #91011 in Electricity and Magnetism for Unfortunate Howdy

Question

An electron is in two separate electric fields, one that is 1500 N/C West and one that is 2000N/C North. If the mass of an electron is 9.1 x 10^-31kg, find the acceleration of the electron.

Answer 1

As long as both electric field vectors are perpendicular to each other, the resulting field can be obatined by means of a Pythagorean theorem:

$$E=\sqrt{E_1^2 + E_2^2}$$

One can also mention that direction of this resulting field is somewhere in the North-Western direction (not needed for the solution of the current problem).

The magnitude of the electrostatic force acting on the electron is

$$F = eE$$

which is oriented in the opposite to the field direction. As it is also the net force, one can apply the 2nd Newton's law:

$$F = m a$$

Hence, we obtain:

$$a = \frac{e E}{m} = \frac{ e \sqrt{E_1^2 + E_2^2}}{m}$$

Substituting the numerical values, we obtain:

$$a = \frac{1.6 \cdot 10^{-19} \sqrt{1500^2 + 2000^2}}{9.1 \cdot 10^{-31}} \approx 4.4 \cdot 10^{14} \, m/s^2$$

Answer: 4.4*10¹⁴ m/s²