Question

The electric field in a region of space is given by, `vec"E"= "E"_"o"hat"i" + 2"E"_"o"hat"j"` where E_o = 100 N/C. The flux of the field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly ______.

Options

• 0.125 Nm²/C

• 0.02 Nm²/C

• 0.005 Nm²/C

• 3.14 Nm²/C

Answer 1

The electric field in a region of space is given by, `vec"E"= "E"_"o"hat"i" + 2"E"_"o"hat"j"` where E_o = 100 N/C. The flux of the field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly 0.125 Nm²/C.

Explanation:

`vec"E"="E"_0"i"+2"E"_0hat"j"`

Given, E₀ = 100 N/c So, `vec"E"=100hat"i"+200hat"j"` 

Radius of circulars surface = 0.02 m

Area  = πr²   

= `22/7xx0.02xx0.02`

= `1.25xx10^-3  hat"i"  "m"^2` [Loop is parallel to Y-Z plane]

Now, flux (Φ) = EA = cosθ

= `(100hat"i"+200hat"j").1.25xx10^-3  hat"i"` cosθ° [θ = 0°]

= 125 × 10^-3 Nm²/C

= 0.125 Nm²/C