Direction of the induced electric field?

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A time-varying magnetic field directed downwards induces an electric field in the horizontal plane, perpendicular to the magnetic field. The direction of the induced electric field can be determined using Faraday's law, which states that the induced electric field is related to the rate of change of magnetic flux. The induced electric field lines form closed loops, and their direction is influenced by the sign of the change in magnetic flux. Factors such as the orientation of the magnetic field and the rate of change of flux determine the specific direction of the electric field. Understanding these principles is crucial for applications in electromagnetism.
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If a time varying magnetic field exists in vertically downwards direction in a region A, an electric field is induced in the direction perpendicular to it i.e. in horizontal plane. How to find the direction of the E field in the horizontal plane?What factors decide the direction of the E field?

Once in a book I read that the E field lines form closed loops. If that is true practically then what factors decide the center of the closed loop? Or is the E field induced is just randomly directed?
 
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Do you know Faraday's law? It says that ##\int{\vec{E}.d\vec{l}}## = -##\frac{∂Φ}{∂t}## where Φ is the magnetic flux. So the direction of the induced electric field is dependent on the sign of the change in magnetic flux.
 
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