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CBSE Class 12 Physics 2014 Delhi Set 2 Paper

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Question : 5 of 8
Marks: +1, -0
Given a uniform electric field E⃗=2×103 i^ N/C\vec{E}=2\times10^{3}\,\hat{i}\,\text{N}/\text{C}. Find the flux of this field through a square of side 20 cm20\text{ cm}, whose plane is parallel to the Y−ZY-Z plane. What would be the flux through the same square, if the plane makes an angle of 30∘30^{\circ} with the XX-axis?
Solution:  
(a) The plane of the square is parallel to the y−zy-z plane. Hence, angle between the unit vector normal to the plane and electric field, θ=0∘\theta=0^{\circ}
Flux (ϕ) through the plane is given by the relation,
ϕ  =∣E⃗∣Acos⁡θ\phi\;=|\vec{E}| A \cos \theta
  =2×103×0.04×cos⁡0∘\;=2\times10^{3}\times0.04\times\cos0^{\circ}
  =80 N m2/C\;=80\,\text{N}\,\text{m}^2/\text{C}
(b) Plane makes an angle of 30∘30^{\circ} with the xx-axis. Hence, angle between the unit vector normal to the plane and electric field, θ=60∘\theta=60^{\circ}
Flux, ϕ  =∣E⃗∣Acos⁡θ\phi\;=|\vec{E}| A \cos \theta
  =2×103×0.04×cos⁡60∘\;=2\times10^{3}\times0.04\times\cos60^{\circ}
  =40 N m2/C\;=40\,\text{N}\,\text{m}^2/\text{C}
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