An infinitely long solid cylinder of radius 190 cm has a non...

An infinitely long solid cylinder of radius 19.0 cm has a non-uniform volume charge density of Ï = 4r^3, where Ï is in C/m^3 when r is in meters. Calculate the magnitude of the electric field at a distance of 10.00 cm from the axis of the cylinder.

Transcript

00:01 Hello, the question is taken from physics and the question is an infinite long cylinder given that an infinite long cylinder.

00:13 This is infinite long cylinder of radius 19 centimetre given that the radius is equal to 19 centimeter and a known uniform charge density of given that row is equal to 4 r cube by 3.

00:32 That is already given to us r is in meter calculate the magnitude of electric field at a distance 10 centimeter from the axis of cylinder so we need to find the electric field inside the cylinder so this is what is the value of electric field at this distance which is at 10 centimeter okay so now in order to evaluate the electric field at this position it is already given to us the charge density so the total charge will be q is equal to r into dv in this radius in radius of r so that will be r and the radius will be 4x2xr into d r sorry this is not circular that is 2 pi r r into d r okay and we know that electric field at a particular distance e will be equal to q by 4 pi epsilon out into r square and the value of q are we already know that is 2 pi r square over into 2 pi r square into what we want that is in final 2 pi r square into d r divided by 4 pi a epsilon out r square okay that is for adias r so this will be cancelled out now we want the electric field at this location due to whole of this charge inside it.

02:13 So, so electric field due to the complete surface is equal to q by 4 pi epsilon not capital r square.

02:23 Now for adias r square will be so that is capital r square for surface value so this will be maximum is on the surface that we already know.

02:38 So this will be square divided by capital r square okay so but we want the electric field inside okay and so that will be so that is two pi capital r square so a volume of a volume of this uh i think the the one that i was doing was correct harrow into two pi r square into d r and r square due due to central current carrying wire.

03:24 Okay...

Question

An infinitely long solid cylinder of radius 19.0 cm has a non-uniform volume charge density of Ï = 4r^3, where Ï is in C/m^3 when r is in meters. Calculate the magnitude of the electric field at a distance of 10.00 cm from the axis of the cylinder.

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An infinitely long solid cylinder of radius 19.0 cm has a non-uniform volume charge density of Ï = 4r^3, where Ï is in C/m^3 when r is in meters. Calculate the magnitude of the electric field at a distance of 10.00 cm from the axis of the cylinder.