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Question
Given a uniform electric field `vecE=5xx10^3hati`N/C, find the flux of this field through a square of 10 cm on a side whose plane is parallel to the y-z plane. What would be the flux through the same square if the plane makes a 30° angle with the x-axis ?
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Solution
When the plane is parallel to the y-z plane:
Electric flux, `phi=vecE.vecA`
Here:
`vecE=5xx10^3hati "N/C"`
`vecA=(10cm^2)hati=10^(-2)hatim^2`
`:.phi=(5xx10^3hati).(10^(-2)hati)`
⇒ ϕ =50 Weber
When the plane makes a 30° angle with the x-axis, the area vector makes 60° with the x-axis.
`phi=vecE.vecA`
⇒ϕ=EA cosθ
⇒ϕ=(5×103)(10−2)cos60°
`=>phi=50/2`
⇒ ϕ =25 Weber
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