Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by:

(A)
(B)
(C)
(D)

Option 1 -

$\dfrac{\sigma}{2\epsilon_0} \left[(1 - \sqrt{3}) \hat{y} - \tfrac{1}{2} \hat{x}\right]$

Option 2 -

$\dfrac{\sigma}{2\epsilon_0} \left[(1 + \sqrt{3}) \hat{y} - \tfrac{1}{2} \hat{x}\right]$

Option 3 -

$\dfrac{\sigma}{2\epsilon_0} \left[(1 + \sqrt{3}) \hat{y} + \tfrac{1}{2} \hat{x}\right]$

Option 4 -

$\dfrac{\sigma}{2\epsilon_0} \left[(1 + \sqrt{3}) \hat{y} + \tfrac{1}{2} \hat{x}\right]$

3 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

$\frac {I_0} {10} = I_0 \cos^2 \theta$ $\cos \theta = \frac {1} {\sqrt {10} = 0.31 < \frac {1} {\sqrt {2} \quad \text {which is 0.707}$

So,

$\theta > 45^\circ \quad \text {and} \quad 90^\circ - \theta < 45^\circ$

so only one option is correct i.e. 18.4°

Angle rotated should be

$= 90^\circ - 71.6^\circ = 18.4^\circ$

Answer: (A) 18.4°

I=I0? cos2? <math ><semantics><mrow><mfrac><msub><mi>I</mi><mn>0</mn></msub><mn>10</mn></mfrac><mo>=</mo><msub><mi>I</mi><mn>0</mn></msub><msup><mrow><mi>cos</mi><mo>? </mo></mrow><mn>2</mn></msup><mi>? </mi></mrow><annotation encoding="application/x-tex">\frac {I_0} {10} = I_0 \cos^2 \theta</annotation></semantics></math>10I0? =I0? cos2? <math ><semantics><mrow><mi>cos</mi><mo>? </mo><mi>? </mi><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>10</mn></msqrt></mfrac><mo>=</mo><mn>0.31</mn><mo><</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mspace width="1em"></mspace><mtext>which is 0.707</mtext></mrow><annotation encoding="application/x-tex">\cos \theta = \frac {1} {\sqrt {10} = 0.31 < \frac {1} {\sqrt {2} \quad \text {which is 0.707}</annotation></semantics></math>cos? =10?1? =0.31<2?1? which is 0.707So, <math ><semantics><mrow><mi>? </mi><mo>></mo><msup><mn>45</mn><mo>? </mo></msup><mspace width="1em"></mspace><mtext>and</mtext><mspace width="1em"></mspace><msup><mn>90</mn><mo>? </mo></msup><mo>? </mo><mi>? </mi><mo><</mo><msup><mn>45</mn><mo>? </mo></msup></mrow><annotation encoding="application/x-tex">\theta > 45^\circ \quad \text {and} \quad 90^\circ - \theta < 45^\circ</annotation></semantics></math>? >45? and90? <45? so only one option is correct i.e. 18.4°Angle rotated should be<math ><semantics><mrow><mo>=</mo><msup><mn>90</mn><mo>? </mo></msup><mo>? </mo><msup><mn>71.6</mn><mo>? </mo></msup><mo>=</mo><msup><mn>18.4</mn><mo>? </mo></msup></mrow><annotation encoding="application/x-tex">= 90^\circ - 71.6^\circ = 18.4^\circ</annotation></semantics></math>=90?71.6? =18.4? Answer: (A) 18.4°

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Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by:

(A)
(B)
(C)
(D)

1 Answer

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Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by: (A) (B) (C) (D)

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Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by:

(A)
(B)
(C)
(D)