Question

A charge Q is given to wires of length A and B in such a way that their linear charge density are same . find the charge on the wires .​

Answer 1

Answer:

A wire of linear charge density λ passes through a cuboid of length ℓ, breadth b and height h (ℓ>b>h) in such a manner that flux through the cuboid is maximum. The position of the wire is now changed, so that the flux through the cuboid is minimum. The ratio of maximum flux to minimum flux will be :

a wire of length L and linear charge density is λ = Kx

we know,

linear charge density means charge per unit length.

so, we can say, λ = dQ/dx

⇒ dQ = λ.dx

⇒ ∫dQ = ∫Kx.dx [∵ λ = Kx ]

⇒ \bold{ \int\limits^Q_0 {dQ} \, =\int\limits^L_0{Kx

⇒ Q = KL²/2

now, according to Gaussian theorem,

Ф = Q/ε₀

here, Ф is electric flux, Q is net charge inclosed in Gaussian surface and ε₀ is permitivity of medium [vaccum]

so, Ф = KL²/2ε₀

Explanation:

Hope it's helpful for you

↓↓↓↓↓↓↓↓