Enter any three inputs and click on Calculate button
How to use this Coulomb's Law Calculator 🤔
There are input fields for Charge \((q₁)\), Charge \((q₂)\), Distance \((r)\), Coulomb's constant \((k)\), and Electrostatic Force \((F)\). Enter any three inputs and click on Calculate button.
The calculator uses the \(F = k \cdot \frac{ q₁ \cdot q₂ }{ r ^2 } \) formula, substitues given values, and calcuates the missing value(s).
A missing value is calcuated and displayed in the input field. Also, the caculation is displayed under the input section.
What is Coulomb's Law?
Coulomb's Law describes the force of attraction or repulsion between two charged particles. It states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law helps us understand the behavior of electric charges.
Calculating the Force Between Two Charges
The force (F) between two charges can be calculated using the formula:
\( F = k \cdot \frac{ q_1 \cdot q_2 }{ r^2 } \).
In this formula, the parameters are defined as follows:
k: Coulomb's constant, a proportionality constant with a value of approximately \( 8.9875 \times 10^9 \) N·m²/C².
q1 and q2: The magnitudes of the two charges, measured in coulombs (C).
r: The distance between the two charges, measured in meters (m).
Input and Output Combinations of the Coulomb's Law Calculator
Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.
Calculator InputsSet #1
q₁ Charge
q₂ Charge
r Distance
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Electrostatic Force\(F = \)\( k \cdot \frac{ q₁ \cdot q₂ }{ r ^2 } \)
{
"topic": "coulombs-law",
"input_types": [
"float",
"float",
"float",
"constant",
"float"
],
"input_labels": [
"q₁",
"q₂",
"r",
"k",
"F"
],
"input_descriptions": [
"Charge",
"Charge",
"Distance",
"Coulomb's constant",
"Electrostatic Force"
],
"input_descriptions_long": [
"magnitude of charge on first object",
"magnitude of charge on second object",
"distance between the two objects",
"Coulomb's constant",
"Electrostatic Force between the two charges"
],
"input_units": [
"C",
"C",
"m",
"N.m<sup>2</sup>/C<sup>2</sup>",
"N"
],
"input_values": [
"",
"",
"",
"8.98755E9",
""
],
"formula_mathjax": "\\(F = k \\cdot \\frac{ q₁ \\cdot q₂ }{ r ^2 } \\)",
"input_pre_msg": "Enter any three inputs and click on Calculate button",
"type": "Calculate",
"title": "Coulomb's Law Calculator",
"description": "Calculate the electrostatic force between two charged objects using our Coulomb's Law Calculator. Input the charge values and the distance between them to get instant results. Ideal for physics students and professionals.",
"category": "Electricity",
"template": "physics",
"precision": 10,
"formulas": [
{
"parameters": [
"q₁",
"q₂",
"r"
],
"outputs": [
{
"label": "F",
"formula": " 8.98755E9 * ( q₁ * q₂ )/ ( r * r )",
"formula_mathjax": "\\( k \\cdot \\frac{ q₁ \\cdot q₂ }{ r ^2 } \\)",
"formula_mathjax_sub": "\\( 8.98755 \\times 10^9 \\times \\frac{ q₁ \\times q₂ }{ r ^2 } \\)"
}
],
"example_heading": "What is the Electrostastic Force between two objects charged at _q₁_ and _q₂_ respectively, and are separated by a distance of _r_ ?",
"examples": [
{
"q₁": 0.01,
"q₂": 0.0001,
"r": 10,
"F": "89.8755"
},
{
"q₁": 0.000001,
"q₂": 1e-7,
"r": 2,
"F": "0.0002"
}
]
},
{
"parameters": [
"q₁",
"q₂",
"F"
],
"outputs": [
{
"label": "r",
"formula": "Math.sqrt( 8.98755E9 * ( q₁ * q₂ )/ F )",
"formula_mathjax": "\\( \\sqrt{ k \\cdot \\frac{ q₁ \\cdot q₂ }{ F } }\\)",
"formula_mathjax_sub": "\\( \\sqrt{ 8.98755 \\times 10^9 \\times \\frac{ q₁ \\times q₂ }{ F } } \\)"
}
],
"example_heading": "Calculate the distance between two objects charged at _q₁_ and _q₂_ respectively, and the electrostatic force between these two objects is _F_ ?",
"examples": [
{
"q₁": 2,
"q₂": 5,
"F": 89875,
"r": "1000.0028"
}
]
}
],
"content": "<h2>What is Coulomb's Law?</h2><p>Coulomb's Law describes the force of attraction or repulsion between two charged particles. It states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law helps us understand the behavior of electric charges.</p><h2>Calculating the Force Between Two Charges</h2><p>The force (<strong>F</strong>) between two charges can be calculated using the formula:</p><p class=\"formula_highlite\">\\( F = k \\cdot \\frac{ q_1 \\cdot q_2 }{ r^2 } \\).</p><p>In this formula, the parameters are defined as follows:</p><ul><li><strong>k</strong>: Coulomb's constant, a proportionality constant with a value of approximately \\( 8.9875 \\times 10^9 \\) N·m²/C².</li><li><strong>q<sub>1</sub></strong> and <strong>q<sub>2</sub></strong>: The magnitudes of the two charges, measured in coulombs (C).</li><li><strong>r</strong>: The distance between the two charges, measured in meters (m).</li></ul><br><h2>Input and Output Combinations of the Coulomb's Law Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">q₁</span> Charge</li><li><span class=\"input\">q₂</span> Charge</li><li><span class=\"input\">r</span> Distance</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Electrostatic Force</span><span class=\"output\">\\(F = \\)\\( k \\cdot \\frac{ q₁ \\cdot q₂ }{ r ^2 } \\)</span></li></ul><a class=\"button\" href=\"#example_1\">2 Examples</a></div><div class=\"formula_set set_2\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #2</span><ul class=\"given\"><li><span class=\"input\">q₁</span> Charge</li><li><span class=\"input\">q₂</span> Charge</li><li><span class=\"input\">F</span> Electrostatic Force</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Distance</span><span class=\"output\">\\(r = \\)\\( \\sqrt{ k \\cdot \\frac{ q₁ \\cdot q₂ }{ F } }\\)</span></li></ul><a class=\"button\" href=\"#example_3\">1 Example</a></div></div><br><br><h2>Examples</h2>\n <div id=\"example_1\" class=\"example\">\n <span class=\"example_n\">1</span>\n <h3 class=\"question\">\n What is the Electrostastic Force between two objects charged at <strong>0.01 C</strong> and <strong>0.0001 C</strong> respectively, and are separated by a distance of <strong>10 m</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>magnitude of charge on first object, q₁ = 0.01 C</li><li>magnitude of charge on second object, q₂ = 0.0001 C</li><li>distance between the two objects, r = 10 m</li></ul>\n <p>Calculating electrostatic force (F)...</p><p class=\"step\">\\( F = \\) \\( k \\cdot \\frac{ q₁ \\cdot q₂ }{ r ^2 } \\)</p><p class=\"step\">\\( F = \\) \\( 8.98755 \\times 10^9 \\times \\frac{0.01\\times0.0001}{10^2 } \\)</p><p class=\"step answer\">\\( F = \\) 89.8755 N</p>\n </div>\n \n <div id=\"example_2\" class=\"example\">\n <span class=\"example_n\">2</span>\n <h3 class=\"question\">\n What is the Electrostastic Force between two objects charged at <strong>0.000001 C</strong> and <strong>1e-7 C</strong> respectively, and are separated by a distance of <strong>2 m</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>magnitude of charge on first object, q₁ = 0.000001 C</li><li>magnitude of charge on second object, q₂ = 1e-7 C</li><li>distance between the two objects, r = 2 m</li></ul>\n <p>Calculating electrostatic force (F)...</p><p class=\"step\">\\( F = \\) \\( k \\cdot \\frac{ q₁ \\cdot q₂ }{ r ^2 } \\)</p><p class=\"step\">\\( F = \\) \\( 8.98755 \\times 10^9 \\times \\frac{0.000001\\times1e-7}{2^2 } \\)</p><p class=\"step answer\">\\( F = \\) 0.0002 N</p>\n </div>\n \n <div id=\"example_3\" class=\"example\">\n <span class=\"example_n\">3</span>\n <h3 class=\"question\">\n Calculate the distance between two objects charged at <strong>2 C</strong> and <strong>5 C</strong> respectively, and the electrostatic force between these two objects is <strong>89875 N</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>magnitude of charge on first object, q₁ = 2 C</li><li>magnitude of charge on second object, q₂ = 5 C</li><li>Electrostatic Force between the two charges, F = 89875 N</li></ul>\n <p>Calculating distance (r)...</p><p class=\"step\">\\( r = \\) \\( \\sqrt{ k \\cdot \\frac{ q₁ \\cdot q₂ }{ F } }\\)</p><p class=\"step\">\\( r = \\) \\( \\sqrt{ 8.98755 \\times 10^9 \\times \\frac{2\\times5}{89875} } \\)</p><p class=\"step answer\">\\( r = \\) 1000.0028 m</p>\n </div>\n <br><h2>Input and Output Combinations of the Coulomb's Law Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">q₁</span> Charge</li><li><span class=\"input\">q₂</span> Charge</li><li><span class=\"input\">r</span> Distance</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Electrostatic Force</span><span class=\"output\">\\(F = \\)\\( k \\cdot \\frac{ q₁ \\cdot q₂ }{ r ^2 } \\)</span></li></ul><a class=\"button\" href=\"#example_1\">2 Examples</a></div><div class=\"formula_set set_2\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #2</span><ul class=\"given\"><li><span class=\"input\">q₁</span> Charge</li><li><span class=\"input\">q₂</span> Charge</li><li><span class=\"input\">F</span> Electrostatic Force</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Distance</span><span class=\"output\">\\(r = \\)\\( \\sqrt{ k \\cdot \\frac{ q₁ \\cdot q₂ }{ F } }\\)</span></li></ul><a class=\"button\" href=\"#example_3\">1 Example</a></div></div><br><br><h2>Examples</h2>\n <div id=\"example_1\" class=\"example\">\n <span class=\"example_n\">1</span>\n <h3 class=\"question\">\n What is the Electrostastic Force between two objects charged at <strong>0.01 C</strong> and <strong>0.0001 C</strong> respectively, and are separated by a distance of <strong>10 m</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>magnitude of charge on first object, q₁ = 0.01 C</li><li>magnitude of charge on second object, q₂ = 0.0001 C</li><li>distance between the two objects, r = 10 m</li></ul>\n <p>Calculating electrostatic force (F)...</p><p class=\"step\">\\( F = \\) \\( k \\cdot \\frac{ q₁ \\cdot q₂ }{ r ^2 } \\)</p><p class=\"step\">\\( F = \\) \\( 8.98755 \\times 10^9 \\times \\frac{0.01\\times0.0001}{10^2 } \\)</p><p class=\"step answer\">\\( F = \\) 89.8755 N</p>\n </div>\n \n <div id=\"example_2\" class=\"example\">\n <span class=\"example_n\">2</span>\n <h3 class=\"question\">\n What is the Electrostastic Force between two objects charged at <strong>0.000001 C</strong> and <strong>1e-7 C</strong> respectively, and are separated by a distance of <strong>2 m</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>magnitude of charge on first object, q₁ = 0.000001 C</li><li>magnitude of charge on second object, q₂ = 1e-7 C</li><li>distance between the two objects, r = 2 m</li></ul>\n <p>Calculating electrostatic force (F)...</p><p class=\"step\">\\( F = \\) \\( k \\cdot \\frac{ q₁ \\cdot q₂ }{ r ^2 } \\)</p><p class=\"step\">\\( F = \\) \\( 8.98755 \\times 10^9 \\times \\frac{0.000001\\times1e-7}{2^2 } \\)</p><p class=\"step answer\">\\( F = \\) 0.0002 N</p>\n </div>\n \n <div id=\"example_3\" class=\"example\">\n <span class=\"example_n\">3</span>\n <h3 class=\"question\">\n Calculate the distance between two objects charged at <strong>2 C</strong> and <strong>5 C</strong> respectively, and the electrostatic force between these two objects is <strong>89875 N</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>magnitude of charge on first object, q₁ = 2 C</li><li>magnitude of charge on second object, q₂ = 5 C</li><li>Electrostatic Force between the two charges, F = 89875 N</li></ul>\n <p>Calculating distance (r)...</p><p class=\"step\">\\( r = \\) \\( \\sqrt{ k \\cdot \\frac{ q₁ \\cdot q₂ }{ F } }\\)</p><p class=\"step\">\\( r = \\) \\( \\sqrt{ 8.98755 \\times 10^9 \\times \\frac{2\\times5}{89875} } \\)</p><p class=\"step answer\">\\( r = \\) 1000.0028 m</p>\n </div>\n "
}
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