Question : An electric filed is uniform and acts along +x direction in the region of positive x. It is also uniform with the same magnitude but acts in -x direction in the region of negative x. The value of the field is E=200 N/C for x>0 and E=-200 N/C for x<0. A right circular cylinder of length 20 cm and radius 5 cm has its centre at the origin and its axis along the x-axis so that one flat surface is at x=+10 cm and the other is at x=-10cm.
Find :
i) The net outward flux through the cylinder.
ii) The net charge present inside the cylinder.
Doubt by Safir
Solution :
E = 200 N/C
r= 5 cm
r=0.05 m
A=πr2
A=π(0.05)
A=0.0025π m2
i) Total Electric flux through the curved surface area of the cylinder will be zero because θ=90° and cos90° is 0.
Electric Flux coming out of the cylinder through the flat side on the +x -axis.
Φ1=EAcosθ
Electric Flux coming out of the cylinder through the flat side on the -x -axis.
Φ2=EAcosθ
Total flux coming out of cylinder
Φ=Φ1+Φ2
Φ=EAcosθ+EAcosθ
Φ=2EAcosθ
Φ=2(200)0.0025πcos0°
Φ=400×0.0025π×1
Φ=π
Φ=3.14 Nm2/C
ii) Using Gauss's Theorem
Φ = qnet/ε₀
qnet=Φ×ε₀
qnet=3.14×8.85×10-12
qnet=27.789×10-12
qnet=2.8×10-11 C
