Find the electric field on the axis of a uniformly charged disc.

Question

Toppr Admin · Accepted Answer

Consider a disc of uniform surface charge density σ .Let us calculate the electric field due to a charged ring of radius r , from the centre and having a width, dr. Here we are using the expression for electric field intensity for a charged ring of radius r at a point on the axis at a distance x from the centre, E =  kxq(x^2 + r^2)^3/2 directed along the axis outwards from the centre.Thus electric field due to elementary ring, dE =  kx dq(x^2 + r^2)^3/2 , directed along the line OP .Now, the area of the ring, dS = 2pi r.dr. Charge on the elementary ring  dq = σ 2pi ede ,Thus, electric field due to entire disc |E|0 = int dE = kx R 0int σ2pirdr(x^2 + r^2)^3/2 =  14pi∈0x.σpi R 0int 2r(x^2 + r^2)^3/2dr E =  σ2∈0 [1 -  x(x^2 + R^2)^1/2 ] =  σ2ε0(1 - costheta) , where theta =  semi vertical angle subtend by the disc at R .Also, as R ⟶∞, E =  σ2∈0 , which is the electric field in front of an infinite plane sheet of charge,

Find the electric field on the axis of a uniformly charged disc.

There is a uniformly charged disc of radius $R 3$ and surface charge density $σ$ work done by electric field to brought a charge $ϱ$ From centre of disc to distance R along its axis will be :-

A thin uniformly charged disc can be imagined as a

An annular disc has inner and outer radius R $_{1}$ and R $_{2}$ respectively. Charge is uniformly distributed. Surface charge density is $σ$ . Find the electric field at any point distant y along the axis of the disc.

A uniformly charged disc has a pin hole at its centre. The electric field at the centre of the disc is zero

Disc can be supported to be made up of many rings. also electric field at the centre of uniformly charged ring is zero

The electric field due to a uniformly charged disc at a point very distant from the surface of the disc is given by
[ $σ$ is the surface charge density on the disc]

Find the electric field on the axis of a uniformly charged disc.

There is a uniformly charged disc of radius R3​ and surface charge density σ work done by electric field to brought a charge ϱ From centre of disc to distance R along its axis will be :-

A thin uniformly charged disc can be imagined as a

An annular disc has inner and outer radius R1​ and R2​ respectively. Charge is uniformly distributed. Surface charge density is σ. Find the electric field at any point distant y along the axis of the disc.

A uniformly charged disc has a pin hole at its centre. The electric field at the centre of the disc is zero

Disc can be supported to be made up of many rings. also electric field at the centre of uniformly charged ring is zero

The electric field due to a uniformly charged disc at a point very distant from the surface of the disc is given by [σ is the surface charge density on the disc]

There is a uniformly charged disc of radius $R 3$ and surface charge density $σ$ work done by electric field to brought a charge $ϱ$ From centre of disc to distance R along its axis will be :-

An annular disc has inner and outer radius R $_{1}$ and R $_{2}$ respectively. Charge is uniformly distributed. Surface charge density is $σ$ . Find the electric field at any point distant y along the axis of the disc.

The electric field due to a uniformly charged disc at a point very distant from the surface of the disc is given by
[ $σ$ is the surface charge density on the disc]