Physics, asked by tejashratme, 1 month ago

two charges of magnitude 3uc and 4uc Columbus kept at (8, 4, 2) and)(0, - 2, 2) respectively find the force between them in vector form​

Answers

Answered by kolamudiutpala
0

Given ,

Δ ABC is a right angled triangle at C

3 uC or 3 × (10)^-6 C charge is located at A

4 uC or 4 × (10)^-6 C charge is located at B

2 C charge is located at C

Distance between A and B is 5 m

Distance between A and C = 3 m

Distance between B and C = 4 m

We know that , the force between two charged particles is given by

\large \mathtt{ \fbox{Force = \frac{k( Q_{1}Q_{2})}{ {(r)}^{2} } }}

Thus ,

\begin{gathered} \sf \hookrightarrow Force \: on \: C \: due \: to \: A = \frac{9 \times {10}^{9} \times 3 \times {(10)}^{ - 6} \times 2 }{ {(3)}^{2} } \\ \\ \sf \hookrightarrow Force \: on \: C \: due \: to \: A = 6 \times {(10)}^{3} \: \: newton \end{gathered}

↪ForceonCduetoA=

(3)

2

9×10

9

×3×(10)

−6

×2

↪ForceonCduetoA=6×(10)

3

newton

and

\begin{gathered} \sf \hookrightarrow Force \: on \: C \: due \: to \: A \: = \frac{9 \times {(10)}^{9} \times 4 \times {(10)}^{ - 6} \times 2 }{ {(4)}^{2} } \\ \\ \sf \hookrightarrow Force \: on \: C \: due \: to \: A \: = \frac{9 \times {(10)}^{3} }{2} \\ \\ \sf \hookrightarrow Force \: on \: C \: due \: to \: A \: = 45 \times {(10)}^{2} \: \: newton\end{gathered}

↪ForceonCduetoA=

(4)

2

9×(10)

9

×4×(10)

−6

×2

↪ForceonCduetoA=

2

9×(10)

3

↪ForceonCduetoA=45×(10)

2

newton

We know that , the resultant between two perpendicular vectors (A and B) is given by

\mathtt{\fbox{Resultant = \sqrt{ {(A)}^{2} + {(B)}^{2} } \: }}

Substitute the known values , we get

\begin{gathered} \sf \hookrightarrow Resultant = \sqrt{ {(6 \times {(10)}^{3} )}^{2} + {(45 \times {(10)}^{2}) }^{2} } \\ \\ \sf \hookrightarrow Resultant = \sqrt{36000000 + 20250000} \\ \\ \sf \hookrightarrow Resultant = \sqrt{56250000} \\ \\ \sf \hookrightarrow Resultant = 7500 \: \: newton\end{gathered}

↪Resultant=

(6×(10)

3

)

2

+(45×(10)

2

)

2

↪Resultant=

36000000+20250000

↪Resultant=

56250000

↪Resultant=7500newton

Hence , the required electrostatics force is 7500 newton

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