Question

Question: Consider one infinitely long straight wire with a uniform charge density of 1C/m. Sketch the electric field around the wire

Question: In the above problem, calculate the magnitude of the electric field at a distance R from the wire. How is it different (if any)from the field of a point charge?

Question: Consider two infinite wires 1 m apart with a uniform charge density per unit length 1 C/m. Calculate the force per unit length between the wires. To do this, just select a tiny, nearly point-like section of a wire of length L and calculate the force due to the electric field of the other wire using the Coulomb’s law. Your answer should be proportional to L. Divide it by L and this is the force per unit length.

Question: Explain, in a few sentences, how the electric force between two charged wires differs from the regular Coulomb law and why.

Question: Consider an infinite non-conducting plane having a charge density of 1 C/m^2. Sketch electric field lines and indicate the value of electric field 1 m away from the plane

Answer 1

Question: (i)

Here, the line has a charge density or uniform charge density () of 1C/m. The field lines will look like the adjacent figure.

Question: (ii)

The electric field of an infinite line charge with a uniform linear charge density can be obtained by a using Gauss' law in electrostatics. Considering a Gaussian surface in the form of a cylinder at radius R and length L, the electric field (E) has the same magnitude at every point of the cylinder and is directed outward. The electric flux () is then just the electric field times the area (A) of the cylinder.

If we consider a point charge (Q), which is equivalent to the net charges included inside the Gaussian surface stated above, will be

Therefore, for R = L/2 the electric field will be same if you place the included charge at a point with distance R.

Question: (iii)

Electric field at any point on the line due to the other line will be

The force per unit length between the wires will be

Question: (iv)

The force is inversely proportional to the separation of line charge. But in case of point charge, the force will be inversely proportional to the square of the separation. As discussed in Q.(ii), you can estimate the force difference between the two cases.

Question: (v)

If you consider a Gaussian surface as a cylinder, the electric field on the curved side will be zero. Electric flux only goes through the circular surface. Hence according to Gauss´s law, you can obtain,

where, R = 1 m is the radius of the cylinder and (1 C/m²) is the surface charge density (here in the above equation I consider the charge density on both side of the surface)

I you put the value of (1 C/m²), the electric field will be