A point charge of 50 μC is placed in the XY plane at a location with radius vector r→0=2i^+3j^ m The electric field strength and its magnitude at a point with radius vector r→=8i^-5j^ m is εo=8.85×10-12 C2 N-m-2

TS EAMCET · Physics · Electrostatics

A point charge of $50 μ C$ is placed in the $X Y$ plane at a location with radius vector ${\vec{r}}_{0} = 2 \hat{i} + 3 \hat{j} m$ The electric field strength and its magnitude at a point with radius vector $\vec{r} = 8 \hat{i} - 5 \hat{j} m$ is $(ε_{o} = 8.85 \times 10^{- 12} C^{2} N - m^{- 2})$

A $4.5 kV m^{- 1}$
B $45 kV m^{- 1}$
C $0.45 kV m^{- 1}$
D $450 kV m^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(A) $4.5 kV m^{- 1}$

Step-by-step Solution

Detailed explanation

Separation vector, =r→-r0→ =8i^-5j^-2i^+3j^ =6i^-8j^ r→-r→0=62+-82=10 Electric field strength, E=14πε0qr2 =14×π×8.85×10-12×50×10-6100 =4495.9 =4.495×103≈4.5 kV m-1

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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