Calculate Electric Field at Point P: L, λ, & Q Given

[Latios1314]

A rod of length L has a uniform positive charge per unit length λ and a
total charge Q as shown in figure below. Calculate the electric field at point P.

http://www.flickr.com/photos/68849979@N03/6261311950/in/photostream"

Been stuck at this question for some time. Could someone point me in the direction as to how should i tackle this question? Great Thanks!

I know I have to solve for both the vertical and horizontal component of E-field. Bu where do i go from there?

 

[Latios1314]

could anyone help me with this question?

 

[SammyS]

A rod of length L has a uniform positive charge per unit length λ and a
total charge Q as shown in figure below. Calculate the electric field at point P.

http://www.flickr.com/photos/68849979@N03/6261311950/in/photostream"

Been stuck at this question for some time. Could someone point me in the direction as to how should i tackle this question? Great Thanks!

I know I have to solve for both the vertical and horizontal component of E-field. Bu where do i go from there?

You need an expression, dE_x for the x-component of the electric field at point (0, -a) due to an element of charge dq at location (x,0) on the x-axis.

You also need an expression for dE_y, the y-component at the same location, due to the same element of charge as above.

To find the electric field, E, integrate each of these components from x = -b, to x = -b+L .

 

[Latios1314]

Managed to find the x-component but I'm having problems with that in the y direction.

I'm taking dE in the y-direction= k dq/ sqrt(x^2+a^2) X a/sqrt(x^2+a^2)

But the answer that i get after integrating it is different from the answer given. Where have i made the mistake?

 

[SammyS]

Managed to find the x-component but I'm having problems with that in the y direction.

I'm taking dE in the y-direction= k dq/ sqrt(x^2+a^2) X a/sqrt(x^2+a^2)

But the answer that i get after integrating it is different from the answer given. Where have i made the mistake?

dE_y should be the negative of that.

What do you get for a result?

What is the given answer?

Added in Edit:

In dE_y: That first sqrt factor should be squared.

 

[vkash]

could anyone help me with this question?

I am going to give you a magic rule(not a magic just metaphor) to solve this kind of question.see this image(in attachment)
electric field due to black charged rod at the point where grey lines meet is equal to the electric field at that point due arc which is intercepted between gray lines.Assume charge density on arc is same as in rod. Center of circle is intersection of grey lines.
Now the question is changed you have to find Electric field at point due to an arc whose chrge density, angle and radius is known.
Now it is quite simple to solve.
This is a fully proved method.

 

[Latios1314]

dE_y should be the negative of that.

What do you get for a result?

What is the given answer?

Added in Edit:

In dE_y: That first sqrt factor should be squared.

dE in the y-direction= k dq/ (x^2+a^2) X a/sqrt(x^2+a^2)

my bad. it should have been this. A typing error. where could the mistake have been made? i got some weird answer after integrating this.