High Voltage Transmission Lines

<...how do we calculate electric field for high voltage transmission lines?...>

Start with "Why?".

Why do you need the charge?

You are talking about electromagnetic field.

read any book on electromagnetic fields and the answer will be there. At least the one by Hayt did have a detailed one in this- _{but that book was in our times},

BTW: EMF is created by moving charge, ie current.

Not entirely correct. In the far field the fields are proportional to current, but the far field of a power line is far enough away no one worries about it. The near field is only of interest under a power line, and there the electric field will be proportional to the potential on the line and the length of the line, which basically means charge. The magnetic field will be proportional only to current, and if it is the magnetic field the OP wants, you are correct.

The magnetic field will be proportional to the effective unbalanced current you see at the distance of separation. Then the magnetic field is just

H = I/2πr,

with H in Amps per meter, I is the unbalanced current, and r is the radial distance from the power line to the point of observation.

By unbalanced current I mean the effective current you see at the point of observation due to incomplete canceling of the fields because you are so close that the field from the closest wire is not completely canceled by the field from the farthest. When you are far away such that your distance of observation is large compared to the separation of the individual wires, then there is little or no unbalanced current and the net magnetic field should be very low.

The electric field is the gradient of the potential along the lines of force between the various three phases and neutral, and ground. If you want a ballpark worst case, just use the potential on the line, divided by the separation between the wire and ground. That is what you would measure directly beneath the line if the line were a single wire working against ground. Since the return current is really carried in the other phases and neutral, this is a worst case calculation.

Again in a balanced phase systems, the sum of the individual voltages will be zero (the phasor sums) and in case of any object such that the distance is sufficiently large with reference to the separation of the lines, this nett electrical field will be zero.

And again since we are not working here with stationary charge, the maxwells equations (for time varying fields will come in picture)

Of course that is unless you are not working with time invariants (HVDC)

Try wikipedia for the basics on electromagnetic theory and the good-old right-hand rule.