A charge q is placed at some distance along the axis of a uniformly charged disc of surface charge density σ. The flux due to the charge q through the disc is φ. The electric force on charge q exerted by the disc is

Question

A charge q is placed at some distance along the axis of a uniformly charged disc of surface charge density σ. The flux due to the charge q through the disc is φ. The electric force on charge q exerted by the disc is (A) σ φ (B) (σ φ/4 π) (C) (σ φ/2 π) (D) (σ φ/3 π)

Tardigrade Admin · Accepted Answer

We know that if a point charge subtends a half-angle

α

on the circular cross-section of a disc, then flux passing through the disc is

ϕ = \frac{q}{2 ε _{o}} (1 - cos α)

Also, if a point charge

q

lies on the axis of a charged disc of charge density

σ

and subtends a half-angle

α

, then it experiences a force

F = \frac{q σ}{2 ε _{o}} (1 - cos α) = σ ϕ

Q. A charge $q$ is placed at some distance along the axis of a uniformly charged disc of surface charge density $σ$ . The flux due to the charge $q$ through the disc is $ϕ$ . The electric force on charge $q$ exerted by the disc is

$σ ϕ$

$\frac{σ ϕ}{4 π}$

$\frac{σ ϕ}{2 π}$

$\frac{σ ϕ}{3 π}$

Q. A charge q is placed at some distance along the axis of a uniformly charged disc of surface charge density σ. The flux due to the charge q through the disc is ϕ. The electric force on charge q exerted by the disc is

σϕ

4πσϕ​

2πσϕ​

3πσϕ​

Q. A charge $q$ is placed at some distance along the axis of a uniformly charged disc of surface charge density $σ$ . The flux due to the charge $q$ through the disc is $ϕ$ . The electric force on charge $q$ exerted by the disc is

$σ ϕ$

$\frac{σ ϕ}{4 π}$

$\frac{σ ϕ}{2 π}$

$\frac{σ ϕ}{3 π}$