The electric field Ein volts-meter at the point 1-1-0 due to point charge of -1 - C located at -1-1-1 co-ordinates in meters is

R=[1 ( 1)]î+(1 1)ĵ+(0 1)k̂ r=2î k̂ Distance between (1,1,0) and ( 1,1,1) = r =√((1 ( 1))^2+(1 1)^2+(0 1)^2)=√(5) E =Q4πϵ nbsp; nbsp;_0r^3(r)=10^ 64πϵ nbs ...

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Electric field due to Charge Distribution - I

The electric ...

Question

The electric field $\to E$ (in volts/meter) at the point (1,1,0) due to point charge of $+ 1 μ C$ located at (-1,1,1) (co-ordinates in meters) is

\frac{10^{- 6}}{20 \sqrt{5} π ε_{0}} (2 i - k)

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\frac{10^{- 6}}{20 π ε_{0}} (2 i - k)

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\frac{- 10^{- 6}}{20 \sqrt{5} π ε_{0}} (2 i - k)

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\frac{- 10^{- 6}}{20 π ε_{0}} (2 i - k)

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Solution

The correct option is A $\frac{10^{- 6}}{20 \sqrt{5} π ε_{0}} (2 i - k)$
$\to r = [1 - (- 1)]^i + (1 - 1)^j + (0 - 1)^k$
$\to r = 2^i -^k$
Distance between (1,1,0) and (-1,1,1) = r
$= \sqrt{(1 - (- 1))^{2} + (1 - 1)^{2} + (0 - 1)^{2}} = \sqrt{5}$
$\to E = \frac{Q}{4 π ϵ_{0} r^{3}} (\to r) = \frac{10^{- 6}}{4 π ϵ_{0} \times (\sqrt{5})^{3)}} (2^i -^k)$
$= \frac{10^{- 6}}{20 \sqrt{5} π ϵ_{0}} (2^i -^k)$

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The electric field →E(in volts/meter) at the point (1,1,0) due to point charge of +1μC located at (-1,1,1) (co-ordinates in meters) is

The correct option is A 10−620√5πε0(2i−k)→r=[1−(−1)]^i+(1−1)^j+(0−1)^k →r=2^i−^k Distance between (1,1,0) and (-1,1,1) = r =√(1−(−1))2+(1−1)2+(0−1)2=√5 →E=Q4πϵ0r3(→r)=10−64πϵ0×(√5)3)(2^i−^k) =10−620√5πϵ0(2^i−^k)

The electric field $\to E$ (in volts/meter) at the point (1,1,0) due to point charge of $+ 1 μ C$ located at (-1,1,1) (co-ordinates in meters) is