Give a uniform electric field \overrightarrow{E}=5 \times 10^3 \stackrel{\^}{i} N/C find the flux of this field through a square of 10 {\cm} on a side whose plane is parallel to the {\YZ} plane. What would be the flux through the same square if the plane makes a 30^{\circ} angle with the {\X}-axis?

CBSE Class 12 Physics 2014 Delhi Set 1 Paper

Question : 10

Total: 30

Give a uniform electric field

→

=5×103

N/C find the flux of this field through a square of 10‌cm on a side whose plane is parallel to the YZ plane. What would be the flux through the same square if the plane makes a 30∘ angle with the X-axis?

Solution:

(a) The plane of the square is parallel to the y−z plane. Hence, angle between the unit vector normal to the plane and electric field, θ=0∘
Flux ( Φ) through the plane is given by the relation,
Φ‌=|

→

|A‌cos‌θ
‌=5×103×0.01×cos‌0∘
‌=50Nm2∕C
(b) Plane makes an angle of 30∘ with the x-axis. Hence, angle between the unit vector normal to the plane and electric field, θ=60∘
Flux, Φ‌=|

→

|A‌cos‌θ
‌=5×103×0.01×cos‌60∘
‌=25Nm2∕C

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