Charging a Body by Induction Method and Coulomb's Law

Coloumb's law states that "the force of attraction or repulsion between two charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them." This note provides us an information on charging a body by induction method and coulomb's law

Summary

Coloumb's law states that "the force of attraction or repulsion between two charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them." This note provides us an information on charging a body by induction method and coulomb's law

Things to Remember

Those materials having free electrons are known as conductors. 

Those materials having all bounded electron are called insulators. 

Electric charge per unit area is called surface charge density.

Electric charge has a tendency to accumulate at sharp edges, corners and pointed parts to have high surface charge density there. 

Coloumb's law states that "the force of attraction or repulsion between two charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them."

The dielectric constant or relative permittivity of a medium can be defined as the ratio of the permittivity of a medium and the permittivity of vacuum of free space.

The dielectric constant of a medium can be defined as the ratio between two charges at certain distance in vacuum and the force between the same charges placed at the same distance is such medium.

MCQs

No MCQs found.

Subjective Questions

Q1:

Find the mean.

15, 13, 18, 16, 14, 17, 12


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Given number</p> <p>15, 13, 18, 16, 14, 17, 12</p> <p>Here,</p> <p>Sum of numbers (&sum;x) =15+13+18+16+14+17+12=105</p> <p>Total numbers (n)=7</p> <p>We have,</p> <p>Mean(\(\overline{x}\)) =\(\frac{&sum;x}{n}\)</p> <p>=\(\frac{105}{7}\)</p> <p>=15</p>

Q2:

Find the mean.

10, 18, 12, 30, 22, 14, 13

 


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>The given data is 10, 18, 12, 30, 22, 14, 13</p> <p>Sum of numbers (&sum;x)=10+18+12+30+22+14+13=119</p> <p>Total numbers (n)=7</p> <p>We have,</p> <p>Mean(\(\overline{x}\))=\(\frac{&sum;x}{n}\)</p> <p>=\(\frac{119}{7}\)</p> <p>=17</p>

Q3:

Find the mean of:

84, 91, 88, 94, 91, 105, 98, 85

 


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>The given data is 84, 91, 88, 94, 91, 105, 98, 85</p> <p>Sum of number (&sum;x) = 84+91+88+94+91+105+98+85 = 736</p> <p>Number (n) = 8</p> <p>Now,</p> <p>Mean(\(\overline{x}\)) = \(\frac{&sum;x}{n}\)</p> <p>= \(\frac{736}{8}\)</p> <p>= 92</p>

Q4:

Find the mean of:

45, 35, 37, 32, 47, 38, 39, 36, 34, 37

 


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>The given data is 45, 35, 37, 32, 47, 38, 39, 36, 34, 37</p> <p>Sum of number (&sum;x) = 45+35+37+3+47+38+39+36+34+37 = 380</p> <p>Number (n) =10</p> <p>Now,</p> <p>Mean(\(\overline{x}\)) = \(\frac{&sum;x}{n}\)</p> <p>= \(\frac{380}{10}\)</p> <p>= 38</p>

Q5:

Find the mean of:

105, 108, 112, 106, 120, 108, 112, 110, 100

 


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>The given data is 105, 108, 112, 106, 120, 108, 112, 110, 100</p> <p>Sum of number (&sum;x) = 150+108+112+106+120+108+112+110+100 = 981</p> <p>Number (n) = 9</p> <p>Now,</p> <p>Mean(\(\overline{x}\)) = \(\frac{&sum;x}{n}\)</p> <p>= \(\frac{981}{9}\)</p> <p>= 109</p>

Q6:

The arithmetic mean of 3 numbers is 60. If two of the numbers are 50 and 60, what is the third number?


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Let, the third number be x.</p> <p>Sum of number (&sum;x) = 50 + 60 + x = 110 + x</p> <p>Number (n) = 3</p> <p>Now,</p> <p>Mean = \(\frac{&sum;x}{n}\)</p> <p>or, 60 = \(\frac{110+x}{3}\)</p> <p>or, 110 + x =180</p> <p>or, x = 180 - 110</p> <p>\(\therefore\) x = 70</p> <p>Hence, the third number is 70.</p>

Q7:

The mean of 3, a+2, 8, 12, 2a-1 and 6 is 7, find the value of a.


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Sum of number (&sum;x) =3+a+2+8+12+2a-1+6 = 30+3a</p> <p>Total Number (n) =6</p> <p>Mean(\(\overline{x}\)) = \(\frac{&sum;x}{n}\)</p> <p>or, 7 = \(\frac{30+3a}{6}\)</p> <p>or, 30+3a = 42</p> <p>or, 3a = 42-30</p> <p>or, a = \(\frac{12}{3}\)</p> <p>&there4; a = 4</p>

Q8:

The weight of 40 students of class VIII are given below, find the mean weight.

Weight(kg) 28 30 31 33 35 38
No. of students 3 8 9 7 6 7

Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <table width=""><tbody><tr><td>Weight(kg)(x)</td> <td>No. of students(f)</td> <td>fx</td> </tr><tr><td>28</td> <td>3</td> <td>84</td> </tr><tr><td>30</td> <td>8</td> <td>240</td> </tr><tr><td>31</td> <td>9</td> <td>279</td> </tr><tr><td>33</td> <td>7</td> <td>231</td> </tr><tr><td>35</td> <td>6</td> <td>210</td> </tr><tr><td>38</td> <td>7</td> <td>266</td> </tr><tr><td></td> <td>N=40</td> <td>&sum;fx=1410</td> </tr></tbody></table><p>Now,</p> <p>Mean (\(\overline{x}\)) = \(\frac{&sum;fx}{N}\)</p> <p>= \(\frac{1410}{40}\)</p> <p>= 35.25</p>

Q9:

Find mean from the given table. 

Marks 9   10 12 14 16 18
Total Students 2 2 7 9 8 4

 


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <table width="321"><tbody><tr><td>Marks(x)</td> <td>Total students(f)</td> <td>fx</td> </tr><tr><td>9</td> <td>2</td> <td>18</td> </tr><tr><td>10</td> <td>2</td> <td>20</td> </tr><tr><td>12</td> <td>7</td> <td>84</td> </tr><tr><td>14</td> <td>9</td> <td>126</td> </tr><tr><td>16</td> <td>8</td> <td>128</td> </tr><tr><td>18</td> <td>4</td> <td>72</td> </tr><tr><td>Total</td> <td>N=32</td> <td>&sum;fx=448</td> </tr></tbody></table><p>Here,</p> <p>Mean(\(\overline{x}\)) = \(\frac{&sum;fx}{N}\)</p> <p>= \(\frac{448}{32}\)</p> <p>=14</p>

Q10:

Find mean from the given table. 

Age 9   10  11  12  13  14  15  16 
Number of students 2  10 4 6 2 5 6 5

Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <table width="234"><tbody><tr><td>Age (x)</td> <td>Total students(f)</td> <td>fx</td> </tr><tr><td>9</td> <td>2</td> <td>18</td> </tr><tr><td>10</td> <td>10</td> <td>100</td> </tr><tr><td>11</td> <td>4</td> <td>44</td> </tr><tr><td>12</td> <td>6</td> <td>72</td> </tr><tr><td>13</td> <td>2</td> <td>26</td> </tr><tr><td>14</td> <td>5</td> <td>70</td> </tr><tr><td>15</td> <td>6</td> <td>90</td> </tr><tr><td>16</td> <td>5</td> <td>80</td> </tr><tr><td>Total</td> <td>N=40</td> <td>&sum;fx=500</td> </tr></tbody></table><p>&there4; Arithmetic Mean (\(\overline{x}\)) = \(\frac{&sum;f&times;x}{N}\)</p> <p>= \(\frac{500}{40}\)</p> <p>= 12.5</p> <p></p>

Q11:

Find mean from the given table. 

Wages (In 100) 50  55  60  85  70  75 
Labour 4 8 7 6 9 6

Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <table width="258"><tbody><tr><td>Wages(In 100) (x)</td> <td>Labour(f)</td> <td>f&times;x</td> </tr><tr><td>50</td> <td>4</td> <td>200</td> </tr><tr><td>55</td> <td>8</td> <td>440</td> </tr><tr><td>60</td> <td>7</td> <td>420</td> </tr><tr><td>85</td> <td>6</td> <td>510</td> </tr><tr><td>70</td> <td>9</td> <td>630</td> </tr><tr><td>75</td> <td>6</td> <td>450</td> </tr><tr><td>Total</td> <td>N=40</td> <td>&sum;fx=2650</td> </tr></tbody></table><p></p> <p>\(\therefore\) Arithmetic mean(\(\overline{x}\)) = \(\frac{&sum;f&times;x}{N}\)</p> <p>= \(\frac{2650}{40}\)</p> <p>= 66.25</p>

Q12:

Find mean from the given table. 

x 5 10 15 20 25 30
f   6   3 6 7 4 4

Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <table width="200"><tbody><tr><td>x</td> <td>f</td> <td>fx</td> </tr><tr><td>2</td> <td>12</td> <td>24</td> </tr><tr><td>4</td> <td>8</td> <td>32</td> </tr><tr><td>6</td> <td>9</td> <td>54</td> </tr><tr><td>8</td> <td>10</td> <td>80</td> </tr><tr><td>10</td> <td>6</td> <td>60</td> </tr><tr><td>12</td> <td>5</td> <td>60</td> </tr><tr><td>Total</td> <td>N=30</td> <td>&sum;fx=510</td> </tr></tbody></table><p>\(\therefore\) Arithmetic mean(\(\overline{x}\)) = \(\frac{&sum;f&times;x}{N}\)</p> <p>= \(\frac{510}{30}\)</p> <p>= 17</p> <p></p>

Q13:

Find mean from the given table. 

 x  2 4 6  8 10 12
 f  12 8   9   10 6 5

Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <table width="239"><tbody><tr><td>x</td> <td>f</td> <td>fx</td> </tr><tr><td>2</td> <td>12</td> <td>24</td> </tr><tr><td>4</td> <td>8</td> <td>32</td> </tr><tr><td>6</td> <td>9</td> <td>54</td> </tr><tr><td>8</td> <td>10</td> <td>80</td> </tr><tr><td>10</td> <td>6</td> <td>60</td> </tr><tr><td>12</td> <td>5</td> <td>60</td> </tr><tr><td>Total</td> <td>N = 50</td> <td>&sum;fx = 310</td> </tr></tbody></table><p>\(\therefore\) Arithmetic mean(\(\overline{x}\)) = \(\frac{&sum;fx}{N}\)</p> <p>= \(\frac{310}{50}\)</p> <p>= 6.2</p> <p></p>

Q14:

 The arithmetic mean of 3 numbers is 60. If two of the numbers are 50 and 60, what is the third number?


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Let the third number be x.</p> <p>Mean of 50, 60 and x = \(\frac{</p> <p></p>

Q15:

 The arithmetic mean of 3 numbers is 60. If two of the numbers are 50 and 60, what is the third number?


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Let the third number be x.</p> <p>Mean of 50, 60 and x = \(\frac{ 50 + 60 + x}{3}\)</p> <p>So, 60 = \(\frac{110 + x}{3}\) ( mean= 60 )</p> <p>Or, 110 + x = 180</p> <p>Or, x = 180 - 110 = 70</p> <p>Hence, the third number is 70.</p> <p></p>

Q16:

 Find the arithmetic mean of: 10, 18, 12, 30, 22, 14, 13.


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>The given data is 10, 18, 12, 30, 22, 14, 13.</p> <p>\(\sum\)x = 10 + 18 + 30 + 22 + 14 + 13 = 119</p> <p> n = 7</p> <p>We have, Mean =(\(\overline{x}\)) = \(\sum{\frac{x}{n}}\)</p> <p> = \(\frac{119}{7}\)</p> <p> = 17.</p> <p></p>

Q17:

 The mean of 3, a + 2, 8, 12, 2a - 1,  and 6 is 7, find the value of a.


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Mean of 3, a + 2, 8, 12, 2a-1 and 6 =\(\frac{3 + a + 2 + 8 + 12 + 2a-1 + 6}{6}\)</p> <p> 7 = \(\frac{30 + 3a}{6}\)</p> <p> Or, 30 + 3a = 42</p> <p> Or, 3a = 42 - 30 = 12</p> <p> Or, a = \(\frac{12}{3}\) = 4</p> <p> Therefore, a = 4.</p>

Q18:

Find the mean of the following frequency distribution.

  Age( in years)   14   15   16   17   18
  No of boys   7   5   10   12   6

 


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>According to the question:</p> <table width="297"><tbody><tr><td>Age( in years) (x)</td> <td>No of boys (f)</td> <td>fx</td> </tr><tr><td>14</td> <td>7</td> <td>98</td> </tr><tr><td>15</td> <td>5</td> <td>75</td> </tr><tr><td>16</td> <td>10</td> <td>160</td> </tr><tr><td>17</td> <td>12</td> <td>204</td> </tr><tr><td>18</td> <td>6</td> <td>108</td> </tr><tr><td>Total</td> <td>N = 40</td> <td>\(\sum\)fx=645</td> </tr></tbody></table><p>We have, mean (\(\overline{x}\)) = \(\sum{\frac{x}{N}}\)</p> <p>= \(\frac{645}{40}\)<br><br></p> <p>= 16.125</p> <p>\(\therefor\) Mean(\(\overline{x}\)) = 16.125</p>

Q19:

 Find the mean of the following frequency distribution.

   Weight ( in kg)   28   30   32   34   35   36   40
  No. of students   6   8   12   16   10   6   4

 


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>According to the Table,</p> <table width="398"><tbody><tr><td>Weight ( in kg) (x)</td> <td>No of students (f)</td> <td>fx</td> </tr><tr><td>28</td> <td>6</td> <td>168</td> </tr><tr><td>30</td> <td>8</td> <td>240</td> </tr><tr><td>32</td> <td>12</td> <td>384</td> </tr><tr><td>34</td> <td>16</td> <td>544</td> </tr><tr><td>35</td> <td>10</td> <td>350</td> </tr><tr><td>36</td> <td>6</td> <td>216</td> </tr><tr><td>36</td> <td>4</td> <td>144</td> </tr><tr><td>Total</td> <td>N =62</td> <td>\(\sum\)fx=2046</td> </tr></tbody></table><p>We have, Mean(\(\overline{x}\)) = \(\sum{\frac{x}{N}}\) = \(\frac{2046}{62}\)</p> <p>= 33</p> <p>Therefore, mean(\(\overline{x}\)) = 33</p>

Q20:

 Find the mean of the following frequency  distribution.

  Age   11   12   13   14   15   16
  No of girls   6   7   5   7   3   2

 


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>According to the Table,</p> <table width="255"><tbody><tr><td>Age(x)</td> <td>No of girls(f)</td> <td>fx</td> </tr><tr><td>11</td> <td>6</td> <td>66</td> </tr><tr><td>12</td> <td>7</td> <td>84</td> </tr><tr><td>13</td> <td>5</td> <td>65</td> </tr><tr><td>14</td> <td>7</td> <td>98</td> </tr><tr><td>15</td> <td>3</td> <td>45</td> </tr><tr><td>16</td> <td>2</td> <td>32</td> </tr><tr><td>Total</td> <td>N= 30</td> <td>\(\sum\)fx=390</td> </tr></tbody></table><p>We have mean (\(\overline{x}\)) = \(\sum{\frac{x}{N}}\)</p> <p>= \(\frac{390}{30}\)</p> <p>= 13</p>

Videos

No videos found.

Charging a Body by Induction Method and Coulomb's Law

Charging a Body by Induction Method and Coulomb's Law

Charging a body negatively by induction
Charging a body negatively by induction

Charging a body negatively by using induction method

  • Take an isolated conductor with insulated stand.
  • Bring a glass rod rubbed with silk near one end of an isolated conductor.
  • Connect the remote end of the conductor to the ground with the help of conducting wire. (The process is called grounding or earthing)
  • Induced free charge (positive charge) is neutralized by the flow of electrons from the earth.
  • Cut the grounding/earthing and finally remove the glass rod.
  • The induced bound charge which is negative finally gets distributed throughout the conductor and it is negatively charged.
Charging a body positively by induction
Charging a body positively by induction


Charging a body positively by using induction method

  • Take an isolated conductor with insulated stand.
  • Bring a glass rod rubbed with fur near one end of an isolated conductor.
  • Connect the remote end of the conductor to the ground with the help of conducting wire. (The process is called grounding or earthing)
  • Induced free charge (negative charge) is neutralized by the flow of electrons from the earth.
  • Cut the grounding/earthing and finally remove the glass rod.
  • The induced bound charge which is positive finally gets distributed throughout the conductor and it is positively charged.

Conductors

Those materials having free electrons are known as conductors. Due to the presence of free electrons conductors allows easy flow of electric current through them. Example: metals

Insulators

Those materials having all bounded electron are called insulators. Due to lack of free electrons they do not allow the flow of electric current through them. Examples: non-metals

Electric charge per unit area is called surface charge density.

i.e. surface charge density \(\sigma = \frac{\text{electric charge(q)}}{area(A)}\)

$$\therefore \sigma = \frac {q}{A}$$

Electric charge has a tendency to accumulate at sharp edges, corners and pointed parts to have high surface charge density there. Due to this, the charge can leak by the process of corona discharge.

Difference between electric charge and electric mass

SN electric charge SN electric mass
1 Electric charges are positive as well as -ve. 1 Electric masses are always positive.
2 It is independent of the motion of the charged body. 2

Mass of an object varies relativistically according to the relation $$M=\frac{M_o}{\sqrt{1-\frac{V^2}{C^2}}}$$

where, Mo = mass of the body at rest

M = mass of the body while moving without velocity.
3 Electric charge follows quantization condition. $$\text{i.e.} q = \pm ne$$ 3 Quantization of mass is unknown yet.
4

The force between two charged can be attractive as well as repulsive according to Columb's law.

$$\therefore f = \frac{kq_1q_2}{r^2}$$

 4

The force between two masses as given as Newton's law of gravitation is always attractive.

$$\therefore f = G\frac{M_1M_2}{r^2}$$

Lesson

Fundamental Electrostatic Phenomena

Subject

Physics

Grade

Grade 11

Recent Notes

No recent notes.

Related Notes

No related notes.