Name: Electric Charges and Electric Fields: A Review
Uploaded: 2019-07-19
Duration: 6 min 41 s
Description: In this video, we are going to review the electric charges, the law of charge, conservation of charges and electric field in detail. Watch this to learn more.

Question

ABC

is an equilateral triangle of side

10 m

and

D

is the mid-point of

BC

. Charges of

+ 100, - 100

and

+ 75 μ C

are placed at

B

,

C

and

D

, respectively. Find the force on a

+ 1 μ C

charge placed at

A

.

Accepted Answer

According to figure

$D$

$B$

$= 9 \times 10^{- 3} \times \frac{100}{100} = 9 \times 10^{- 3} N$

$F_{AD} = \frac{1}{4 π ε_{0}} . \frac{75 \times 10^{- 12}}{{(5 \sqrt{3})}^{2}}$ $= \frac{9 \times 10^{9} \times 75 \times 10^{12}}{75}$ $= 9 \times 10^{- 3} N$

If $F_{1}$ be the resultant of $F_{AC}$ and $F_{AB}$ , then $F_{1} = 2 F_{AC} \cdot \cos \frac{120 °}{2}$

$= 2 \times 9 \times 10^{- 3} \times \frac{1}{2}$

$= 9 \times 10^{- 3} N$

Now ${\vec{F}}_{1}$ and ${\vec{F}}_{AD}$ becomes perpendicular to each other because direction of resultant of two equal force is along the bisector of angle between them

$\propto = \frac{Q}{2} = \frac{120 °}{2}$ $= 60 °$

Along the $x - axis$

Here $F_{DA} = 9 \times 10^{- 3} N$

$F_{1} = 9 \times 10^{- 3} N$

If $β$ is the angle between $F_{net}$ and ${\vec{F}}_{1}$ then $\tan β = \frac{F_{DA}}{F_{1}} = \frac{9 \times 10^{- 3}}{9 \times 10^{- 3}}$ $= 1 = \tan 45 °$

$\Rightarrow β = \tan^{- 1} (tan 45°)$ $= 45 °$

The net force acting on A : $\sqrt{{(F_{D A})}^{2} + {(F_{1})}^{2}} = \sqrt{(81 + 81) \times 10^{- 6}}$

$F_{n e t} = 12.73 \times 10^{- 3} N$

$ABC$ is an equilateral triangle of side $10 m$ and $D$ is the mid-point of $BC$ . Charges of $+ 100, - 100$ and $+ 75 μ C$ are placed at $B$ , $C$ and $D$ , respectively. Find the force on a $+ 1 μ C$ charge placed at $A$ .

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

ABC is an equilateral triangle of side 10 m and D is the mid-point of BC. Charges of +100,-100 and +75 μC are placed at B, C and D, respectively. Find the force on a +1 μC charge placed at A.

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

$ABC$ is an equilateral triangle of side $10 m$ and $D$ is the mid-point of $BC$ . Charges of $+ 100, - 100$ and $+ 75 μ C$ are placed at $B$ , $C$ and $D$ , respectively. Find the force on a $+ 1 μ C$ charge placed at $A$ .