Question

In a certain region of space, the electric field always pointing in x-direction but its magnitude decreases from E = 560N/C at
2 = 0 to E = 410N/C at x=25m.if a cubical box of side length 1=25 m is oriented, such that its four sides are parallel to the field
long then charges enclosed by the box is
(A) 8.3 x 10-7
(B) 8.3 x 105c
(C) -8.3 x 10-5C
(D) -8.3 x 10-7c

Answer 1

Torque experienced by the system is zero.

Explanation:

Dipole moment of the system, p = q * dl = - 10^-7 C m

Rate of increase of electric field per unit length = dE/dl = 10^+5 N/C

Force experienced by the system, F = qE

= q.(dE/dl).dl

= p.(dE/dl)

= -10^-7 * 10^5

= -10⁻² N

The force is -10⁻² N. The negative signs denotes the direction of the force which will be in the direction opposite to the direction of the electric field. So, the angle between the electric field and dipole moment is 180°.

Torque (τ)  = pE sin180° = 0

Hence the torque experienced by the system is zero.

Answer 2

1. We have to apply gauss theorem for this particular sum.
2. First, find net flux
3. then apply gauss theorem