A divergenceless field is solenoidal and a curl-free field is irrotational. Given a vector function F=ax (x+3y-c1z)+ay (c2x+5z)+az (2x-c3y+c4z) A) determine c1, c2 and c3 if F is irrotational{CURL FREE}. and B) determine c4 if F is solenoidal{DIVERGENCE FREE}.

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A: Ans (a)-->

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Solenoids

A solenoid is a common term for a telephone coil used as an electromagnet. It also refers to any device that uses a solenoid to convert electrical energy into mechanical energy. The device generates a magnetic field from an electric field and uses the magnetic field to produce precise motion. Solenoid valves are often used to change power, such as in-car transmitters or valves, such as in the fuel system.