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) cos θ (B) cot θ (C) sin θ (D) tan θ

Tardigrade Admin · Accepted Answer

Electric field due to a charged conducting sheet of surface charge density

σ

is given by

E = \frac{σ}{ε _{0} ε _{r}}

where,

ε_{0} =

permittivity in vacuum and

ε_{r}

relative permittivity of medium.
Here, electrostatic force on

B

QE = \frac{Q σ}{ε _{0} ε _{r}}

FB D

of

B

is shown in figure.
In equilibrium,

T cos θ = m g

and

T s in θ = \frac{Q σ}{ε _{0}^{\cdot} ε _{r}}

Thus,

t an θ \propto σ

or

σ \propto t an 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:

$cos θ$

$co t θ$

$s in θ$

$t an θ$

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:

cosθ

cotθ

sinθ

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:

$cos θ$

$co t θ$

$s in θ$

$t an θ$