E-field from Time Varying B-field of Current wire

[kalashbhatt]

Homework Statement

Time Varying Current carrying wire creates time varying magnetic field.How can we analytically calculate electric field at distance r from the time varying current carrying wire?

I(t) is time varying current

where α , β are angle of two ends of current carrying wire.

Homework Equations

B=μ*I(t)(sin(α)+sin(β)/(4*pi) direction given by right hand thumb rule.in Phi direction.
*consider length of wire to very very less than wavelength of changing current.*

The Attempt at a Solution

∇×E=−dB/dt .

dEψ/dz = −dB/dt .

 

[mukundpa]

Faraday's law can be written as

$\oint$$\vec{E}$.$\vec{dl}$ = - d∅/dt