Consider a uniform electric field $E = 3 \times 10^{3} \hat{i} N / C .$ (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane? (b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

Given space space space space space space straight E with rightwards arrow on top space equals space 3 space cross times space 10 cubed space straight i with hat on top space NC to the power of negative 1 end exponent

(a)

increment space straight S space left parenthesis Area space of space the space square right parenthesis space equals space 10 space cross times space 10 space equals space 100 space cm squared space equals space 10 to the power of negative 2 end exponent straight m to the power of negative 2 end exponent

The area of a surface can be represented as a vector along normal to the surface. Since normal to the square is along x-axis, we have

increment straight S with rightwards arrow on top space equals space 10 to the power of negative 2 end exponent space straight i with hat on top space straight m to the power of negative 2 end exponent

Electricity flux through the square

(a) The area of a surface can be represented as a vector along no

equals space open parentheses 3 cross times 10 cubed straight i with hat on top close parentheses. space open parentheses 10 to the power of negative 2 end exponent straight i with overparenthesis on top close parentheses equals space 30 space Nm squared space straight C to the power of negative 1 end exponent

(b) Given, the angle between area vector and the electric field is 60°. Therefore,

straight ϕ space equals space straight E with rightwards arrow on top space. space increment straight S with rightwards arrow on top space space space equals space straight E space. space ds space cos space 60 degree space space space equals space 3 space cross times space 10 cubed cross times 10 to the power of negative 2 end exponent cross times 1 half space space space equals 15 space Nm squared space straight C to the power of negative 1 end exponent space space space space

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Consider a uniform electric field E = 3 ×103 i^ N/C. (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane? (b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

Electric Charges and Fields

Physics Part I

Consider a uniform electric field $E = 3 \times 10^{3} \hat{i} N / C .$ (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane? (b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?