Question

A cube has sides of length L = 1.00 mm. One corner is at the origin. The nonuniform electric
field is given by E~ = (19.00N/C ·m) x ˆi−(1.34N/C ·m) z
ˆk. (a) find the electric flux through
each of the six cube faces S1, S2, S3, S4, S5, S6. (b) Find the total electric charge inside the
cube.

Answer 1

Given that,

E~ = (19.00N/C ·m) x ˆi−(1.34N/C ·m) z k

side = 1 mm = 10^-3 m

Area of any side = (10^-3)² = 10^-6 m²   

(a)We know that flux is given by ; (phi) = E x A.Using thislets find out flux from all the six faces.

flux through face S1 = (phi)1 = E A1 = (-1.34) k (10^-6) (10^-3) k = -1.34 x 10^-9

flux through face S2= (phi)2 = E A2 = (10^-6) j x 0 j = 0

flux through face S3= (phi)3 = E A3 = (-10^-6) k x (-1.34) = 0

flux through face S4= (phi)4= E A4 =  (-10^-6) j x 0 j = 0

flux through face S5= (phi)5 = E A5 = (10^-6) i x (19) i (10^-3)= 19 x 10^-9

flux through face S6= (phi)5 = E A6 =  (-10^-6) i x 19 i = 0

(b) Totak flux =  -1.34 x 10^-9 +  19 x 10^-9 =  17.66 x 10^-9

We know that, total flux = Q enclosed / epsilon0

Q(enclosed) = flux x epsilon 0

Q(enclosed) = 17.66 x 10^-9 x 8.85 x 10^-12 = 1.56 x 10^-19 C

Hence, Q =  1.56 x 10^-19 C