A charged ball B hangs from a silk thread S, which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to

Question

A charged ball B hangs from a silk thread S, which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to (A)  cot θ (B)  cot θ (C)  tan θ (D)  sin θ

Tardigrade Admin · Accepted Answer

In equilibrium T cos θ=m g ...(i) and T sin θ=F=E q T sin θ=F =E q ...(ii) ∴ (T sin θ/T cos θ)=(σ q/2 ε0 × m g) tan θ=(σ q/2 ε0 m g) or σ propto tan θ

Q. A charged ball $B$ hangs from a silk thread $S$ , which makes an angle $θ$ with a large charged conducting sheet $P$ , as shown in the figure. The surface charge density $σ$ of the sheet is proportional to

$cot θ$

$cot θ$

$tan θ$

$sin θ$

In equilibrium
$T cos θ = m g$ ...(i) and $T sin θ = F = Eq$
$T sin θ = F = Eq$ ...(ii)
$∴ \frac{T s i n θ}{T c o s θ} = \frac{σ q}{2 ε _{0} \times m g}$
$tan θ = \frac{σ q}{2 ε _{0} m g}$
or $σ \propto tan θ$

Q. A charged ball B hangs from a silk thread S, which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to

cotθ

cotθ

tanθ

sinθ

In equilibrium Tcosθ=mg ...(i) and Tsinθ=F=Eq Tsinθ=F=Eq ...(ii) ∴TcosθTsinθ​=2ε0​×mgσq​ tanθ=2ε0​mgσq​ or σ∝tanθ

Q. A charged ball $B$ hangs from a silk thread $S$ , which makes an angle $θ$ with a large charged conducting sheet $P$ , as shown in the figure. The surface charge density $σ$ of the sheet is proportional to

$cot θ$

$cot θ$

$tan θ$

$sin θ$

In equilibrium
$T cos θ = m g$ ...(i) and $T sin θ = F = Eq$
$T sin θ = F = Eq$ ...(ii)
$∴ \frac{T s i n θ}{T c o s θ} = \frac{σ q}{2 ε _{0} \times m g}$
$tan θ = \frac{σ q}{2 ε _{0} m g}$
or $σ \propto tan θ$