Two electrostatic forces of magnitude 3.0\text{ N} and 4.0\text{ N} act on a small test ch… — JAMB UTME

Two electrostatic forces of magnitude $3.0\text{ N}$ and $4.0\text{ N}$ act on a small test charge at right angles ( $90^\circ$ ) to each other. What is the magnitude of the net electrostatic force acting on the charge?

A
$7.0\text{ N}$
$5.0\text{ N}$ Answer
C
$1.0\text{ N}$
D
$12.0\text{ N}$

Answer

5.0\text{ N}

The net electrostatic force is found by vector addition. Since the two forces are perpendicular (

90^\circ

), the magnitude of their resultant is given by

\sqrt{F_1^2 + F_2^2} = \sqrt{3.0^2 + 4.0^2} = 5.0\text{ N}

Step-by-Step Solution

Identify the nature of force as a vector quantity.

Electrostatic forces must be combined using vector addition rather than simple scalar addition.

The forces act at right angles (

90^\circ

) to each other.

Apply the Pythagorean theorem to calculate the magnitude of the resultant net force

F_{\text{net}}

F_{\text{net}} = \sqrt{F_1^2 + F_2^2} = \sqrt{3.0^2 + 4.0^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0\text{ N}

For perpendicular vectors, the resultant is the hypotenuse of a right-angled triangle formed by the vector components.

Key Concept

Vector Addition of Electrostatic Forces

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