Find net electric field in a wire?

In summary, the problem involves finding the electric field at a point P due to a wire with length 2a and a perpendicular distance x from the center. The electric field is given by the integral (1/4πε)*(Q/2a)∫x.dy/(x^2+y^2)^3/2, which can be solved using Gauss' law and the relationship between electric flux density and electric field.
  • #1
saba.shahin95
1
0
After solving this problem I ended up with--(2a is the length of the wire)(integral limit is from -a to +a)
(x is the ⊥ distance from centre of the wire to a point P where we have to find the net field )
E[SUBx]= (1/4Πε)*(Q/2a)∫x.dy/(x^2+y^2)^3/2

P.S- sorry, I'm not able to upload the image of the problem. This is my first time ever at this site.
Help me in solving this integral.
Detailed solution would be appreciated . ☺
 
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  • #3
Do you want the electric field in the wire or around the wire at some point in space ##P##? I'm assuming you want the electric field at some point ##P##.

The easiest way to do this problem is to position the wire along the z-axis and enclose it in a cylindrical Gaussian surface. Then using Gauss' law, find the magnitude of the electric flux density ##| \vec D |## in terms of the enclosed charge.

Then using ##\vec D = \varepsilon \vec E##, you will be able to find the electric field.

Hint: The electric flux density ##\vec D## points radially outwards from the cylinder, so in cylindrical co-ordinates we can write it as ##\vec D = |\vec D| \hat r##.
 

1. How do you define electric field in a wire?

The electric field in a wire is a measure of the force per unit charge experienced by a test charge placed at a point in the wire. It is a vector quantity and is defined as the force per unit charge in the direction of the electric field.

2. How do you calculate the net electric field in a wire?

The net electric field in a wire can be calculated by using the equation E = kQ/r^2, where E is the electric field, k is the Coulomb's constant, Q is the charge of the wire, and r is the distance from the wire.

3. What factors affect the net electric field in a wire?

The net electric field in a wire can be affected by various factors such as the charge of the wire, the length of the wire, the distance from the wire, and the surrounding environment. Additionally, the presence of other charges or conductors nearby can also influence the net electric field.

4. How does the direction of the electric field in a wire affect its properties?

The direction of the electric field in a wire determines the direction of the force on a test charge placed at a point in the wire. It also affects the flow of electrons in the wire, which is important for the functioning of various electrical devices and circuits.

5. Can the net electric field in a wire be negative?

Yes, the net electric field in a wire can be negative. This means that the direction of the electric field is opposite to the direction of the force on a positive test charge. It is important to note that the magnitude of the electric field is always positive, but its direction can be negative depending on the charge of the wire and the location of the test charge.

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