Question

Consider a very thin rectangular conducting plate whose length is 109.0 cm, width is 86.0 cm, and has a total charge of −58.0 nC. The plate lies in the horizontal plane (xz plane) and has a uniform charge density. Find the electric field vector at points just above the plate and just below the plate. Express your answer in vector form.

Answer 1

electric field just above the plate is given as

`E = -3495.6 \hat k`

Now electric field just below the plate is given as

`E = 3495.6 \hat k`

Step-by-step explanation:

Charge density of the plates is given as

`\sigma = (Q)/(A)`

here we know that

`Q = -58 nC`

Area = (length)(width)

`A = 1.09* 0.86 m^2`

`A = 0.9374 m^2`

Now we have

`\sigma = (-58 nC)/(0.9374)`

`\sigma = -61.87 nC/m^2`

now electric field due to a thin sheet is given by

`E = (\sigma)/(2\epsilon_0)`

`E = (61.87* 10^(-9))/(2(8.85 * 10^(-12))`

`E = 3495.6 N/C`

Now electric field just above the plate is given as

`E = -3495.6 \hat k`

Now electric field just below the plate is given as

`E = 3495.6 \hat k`