Electric Field due to line charge

[utkarshakash]

Homework Statement

A non-conducting rod AB, having uniformly distributed positive charge of linear charge density λ is kept in x-y plane. The rod AB is inclined at an angle 30° with +ve Y-axis. The magnitude of electrostatic field at origin due to rod AB is E_0 N/C and its direction is along line OC. If line OC makes an angle θ=10a+b degree with negative x-axis as shown in the figure, calculate the value of (a+b) [OA=2m and λ=10^3 C/m]

Homework Equations

Please see the attached diagram

The Attempt at a Solution

$E_x = \dfrac{\lambda}{4 \pi \epsilon _0 d} (\sin 60 + \sin 30) \\ E_y = \dfrac{\lambda}{4 \pi \epsilon _0 d} |\cos 30 - \cos 60| \\ \tan \alpha = \dfrac{E_y}{E_x} \\ =\dfrac{ |\cos 30 - \cos 60| }{(\sin 60 + \sin 30)}$

which comes out to be 15°.

Thus, θ = 30° - 15° = 15°. So, a+b = 6. But it's not the correct answer :(

 

[guitarphysics]

I had a different result for $E_y$ but the same result for $E_x$. How did you arrive at your expressions of the field components? I integrated over the line.

 

[utkarshakash]

I had a different result for $E_y$ but the same result for $E_x$. How did you arrive at your expressions of the field components? I integrated over the line.

I did the integration again and got the expression for E_y as
$\dfrac{\lambda}{16 \pi \epsilon _0 d} (\cos 60^0 - \cos 120^0)$

Do you get the same result?

 

[Vibhor]

A non-conducting rod AB, having uniformly distributed positive charge of linear charge density λ is kept in x-y plane. The rod AB is inclined at an angle 30° with +ve Y-axis. The magnitude of electrostatic field at origin due to rod AB is E_0 N/C and its direction is along line OC. If line OC makes an angle θ=10a+b degree with negative x-axis as shown in the figure, calculate the value of (a+b) [OA=2m and λ=10^3 C/m]

Hi utkarshakash

1. Is θ=10a+b degree given and value of a+b is to be determined ?
2. What are a and b ?
3. What is the answer according to the key ?

Thanks

 

[utkarshakash]

Hi utkarshakash

1. Is θ=10a+b degree given and value of a+b is to be determined ?
2. What are a and b ?
3. What is the answer according to the key ?

Thanks

1. Yes
2. a and b are variables which need to be determined.
3. I don't remember. I posted this a long time ago. I don't have the answer keys right now.

 

[Vibhor]

1. Yes
2. a and b are variables which need to be determined.
3. I don't remember. I posted this a long time ago. I don't have the answer keys right now.

Thank you :)

But I wonder how is this possible . Value of θ can be determined which gives value of (10a+b) ,but then we need another equation in a and b to determine value of (a+b)

Any thoughts ?

 

[utkarshakash]

Thank you :)

But I wonder how is this possible . Value of θ can be determined which gives value of (10a+b) ,but then we need another equation in a and b to determine value of (a+b)

Any thoughts ?

This is an integer type question. This means you'll have to get a and b by trial and error and I don't think it'd be difficult to do so.

 

[Vibhor]

Fine . So a and b are integers . This is what I wanted to know .

Thanks a lot :)