CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Two mutually perpendicular infinite wires carry positive charge densities λ1 and λ2. The electric lines of force makes angle α with second wire then λ1λ2 is

A
tan2α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
cot2α
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
sin2α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
cos2α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B cot2α
The direction of net electric field due to both infinite charged wires will be along the electric lines of force.

The directions of electric fields due to both wires at any point P at distance from the point of intersection of both wires is shown in the given figure.
Here,

E1= electric field due to infinite charged wire of charge density λ1;

E2= electric field due to infinite charged wire of charge density λ2;

So, from the figure,

tanα=E2E1

tanα=2kλ2/r22kλ1/r1 [E=2kλr]

tanα=λ2×r1λ1×r2

tanα=λ2λ1×rcosαrsinα=λ2λ1×cotα

λ1λ2=cot2α

Hence, option (b) is the correct answer.

flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image