wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Two parallel conducting plates have charges on different identical surfaces as shown in the figure. Which of the following statements is/are correct?


A
q1=q3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
q1=q3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
q2=q4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
q2=q1+q42
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C q2=q4
Let q1 be the charge reciding on surface (1), q2 be the charge on surface (2), q3 be the charge on surface (3) and q4 be the charge on surface (4).

Let us take a Gaussian surface as shown in the figure below

Since, no field lines will cut the surfaces AB and CD (as they are parallel to the field lines), so flux through AB and CD surface will be zero.

Also, electric field inside the conductor is zero, so the electric flux through BC and DA will also be zero.

So, from gauss theorem we can conclude that,

ϕnet=qinε0=0

qin=0

From figure, charge enclosed by the Gaussian surface,
qin=q1+q3=0

q1=q3

Let us choose a point P on the surface AC:

As electric field inside the conductor is zero, so |E|p=0

E2=E1+E3+E4

where, E1,E2,E3 and E4 are electric fields due to charges present on face 1,2,3 and 4 respectively.

Since electric field formula due to charge on plate surface,E=Q2Aε0 So, applying above formula for each plate, we get

q22Aε0=q12Aε0+q32Aε0+q42Aε0

where, A is the surface area of plate.

q2=q1+q3+q4

As, q1=q3 we get, q2=q3+q3+q4

q2=q4

Hence, options (b) and (c) are the correct answers.
Note: Students are adviced to memorise these two results, as these are extremly important to solve many other problems.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon