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CBSE Class 12 Physics 2014 Delhi Set 1 Paper

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Question : 10 of 30
Marks: +1, -0
Give a uniform electric field E⃗=5×103i^\vec{E}=5 \times 10^{3} \hat{i} N/C find the flux of this field through a square of 10 cm10\,\mathrm{cm} on a side whose plane is parallel to the YZYZ plane. What would be the flux through the same square if the plane makes a 30∘30^{\circ} angle 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)\Phi) through the plane is given by the relation,
Φ  =∣E⃗∣Acos⁡θ\Phi\; = |\vec{E}| A \cos\theta
  =5×103×0.01×cos⁡0∘\; = 5 \times 10^{3} \times 0.01 \times \cos 0^{\circ}
  =50 N m2/C\; = 50\,\mathrm{N}\,\mathrm{m}^2/\mathrm{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
  =5×103×0.01×cos⁡60∘\; = 5 \times 10^{3} \times 0.01 \times \cos 60^{\circ}
  =25 N m2/C\; = 25\,\mathrm{N}\,\mathrm{m}^2/\mathrm{C}
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