An electron is acted on by two electric forces, one of 2.7*10-14 N acting upward and a second of 5.8*10-14 N acting to the right. What is the magnitude of the electric field at the electron's location?

3.99*10⁵ N/C

Explanation:

Assuming both force forms a right angle triangle,

Using Pythagoras theorem,

a² = b²+c² ... Equation 1

Where a = resultant of the two forces, b = the force acting upward, c = the force acting to the right.

make a the subject of the equation.

a = √ (b²+c²) ... Equation 2

Given: b = 2.7*10⁻¹⁴ N, c = 5.8*10⁻¹⁴ N.

Substitute into equation 2

a = √[ (2.7*10⁻¹⁴) ² + (5.8*10⁻¹⁴) ²]

a = √[7.28*10⁻²⁸) + (33.64*10⁻²⁸) ]

a = √ (40.92*10⁻²⁸)

a = 6.397*10⁻¹⁴ N.

But,

F = Eq ... Equation 3

Where E = Electric Field, q = charge of an electron, F = electric force.

make E the subject of the equation,

E = F/q ... Equation 4

Given: F = 6.397*10⁻¹⁴ N, q = 1.602*10⁻¹⁹ C.

Substitute into equation 4

E = 6.397*10⁻¹⁴ / (1.602*10⁻¹⁹)

E = 3.99*10⁵ N/C