Name: Continuous Charge Distribution
Uploaded: 2019-07-19
Duration: 5 min 39 s
Description: This video will help us understand the necessity of continuous charge distribution and learn about the concept of linear charge density. Learn more.

Question

Three charges of respective values $- \sqrt{2} μ C, 2 \sqrt{2} μ C$ and $- \sqrt{2} μ C$ are arranged along a straight line as shown in the figure. Calculate the total electric field intensity due to all three charges at the point $P$ .

Accepted Answer

From the figure (i) above, the distance between P and B comes to be $\sqrt{1^{2} + 1^{2}} = \sqrt{2} m$ (by Pythagoras theorem). Similarly PD = $\sqrt{2} m$ .

So, $q_{B} = - \sqrt{2} μ C, q_{C} = 2 \sqrt{2} μ C, q_{D} = - \sqrt{2} μ C$

The electric field at P due to charges at B and D will be directed towards B and D as shown in fig (2).

There magnitude will be equal as both has same charge. $E = \frac{k q}{r^{2}}$ where $r$ = PD = PB = $\sqrt{2} m$

The resultant of the two fields( due to charge at A and D) will be in downward direction perpendicular to BD with magnitude $\sqrt{E^{2} + E^{2}} = \sqrt{2} E$

Now the field due to charge at C (in upward direction )and the resultant of charge at A and D, will be in opposite direction.

Thus, $E_{net} = E_{C} - \sqrt{2} E$

or, $E_{net} = \frac{k q_{C}}{1^{2}} - \frac{\sqrt{2} k q_{B}}{{(\sqrt{2})}^{2}} [as q_{B} = q_{D}]$

substituting the values we get,

$E_{net} = 16.46 \times 10^{3} N C^{- 1}$

As we are getting a positive value of $E_{net}$ , it means electric field due to charge at C is greater than the resultant of charges at B and D. Thus resultant electric field is perpendicular and away from line BD.

Three charges of respective values $- \sqrt{2} μ C, 2 \sqrt{2} μ C$ and $- \sqrt{2} μ C$ are arranged along a straight line as shown in the figure. Calculate the total electric field intensity due to all three charges at the point $P$ .

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

Three charges of respective values -2μC, 22μC and -2μC are arranged along a straight line as shown in the figure. Calculate the total electric field intensity due to all three charges at the point P.

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

Three charges of respective values $- \sqrt{2} μ C, 2 \sqrt{2} μ C$ and $- \sqrt{2} μ C$ are arranged along a straight line as shown in the figure. Calculate the total electric field intensity due to all three charges at the point $P$ .