Question

Find the electric flux emanating through a surface element ds=5i, Placed in an electric field E=4i+4j+4k

Answer 1

Answer:

flux is defined as electric field vector dot product with area vector . so

( 4i + 4j + 4k ) . ( 5i ) = 20.. hope this helps..

Answer 2

Electric flux, property of an electric field that may be thought of as the number of electric lines of force (or electric field lines) that intersect a given area. Electric field lines are considered to originate on positive electric charges and to terminate on negative charges.

Formula of electric flux,

$ϕ= E.ds \: \: \: \: \: .....(1)$

$\mathbf {E} = electric field$

$dS = area \: of \: the \: surface$

$\phi = flux \: of \: electric \: field \: \\ through a \: closed \: cylindrical \: surface$

Now we have ,

$E= 4\hat i+ 4\hat j+4\hat k$

$ds = 5 \:\hat i$

Put the given data in equation (1),

$ϕ= E.ds \\ ϕ=(4\hat i+ 4\hat j+4\hat k).(5\hat i)$

From physics , dot product formulas are,

$\hat i \times \hat i = 1 \\ \hat j \times \hat j= 1 \\ \hat k\times \hat k = 1$

So,

$ϕ=(4\hat i).(5\hat i) \\ ϕ=(4 \times 5).(\hat i.\hat i) \\ϕ=20 \: Nm²/C$

Hence ,

The electric flux emanating through a surface is

$ϕ=20 \: Nm²/C$

Project code #SPJ2