Can anyone help me with these problems?
1. Three thin infinite wires carrying currents I go perpendicularly to the paper sheet that they intersect at the points forming an equilateral triangle of side L. Two currents go inside the sheet and one goes out of the sheet. Calculate the absolute value of the magnetic field created by the currents in the middle of each side of the triangle.
2. A flat rectangular coil of the equilateral triangle shape with side a consisting of N loops of wire, carrying a current I is placed in a uniform magnetic field B that is making an angle theta with the normal to the current loop. What is the value of the magnetic moment M of the loop? What is the magnitude of the torque T acting on the loop? In which direction the loop will rotate under the influence of the torque?
3. A coil consisting of N loops of wire with radius R is initially oriented so that its plane is parallel to a magnetic field B. During the time interval delta t, the coil is rotated by the angle theta. what is the average EMF induced in the coil?
4. An electron performs a circular motion in the plane perpendicular to a uniform magnetic field with the radius R= 3 m. What will be the radius if the electron is replaced by a doubly charged helium atom and the magnetic field is increased by a factor of 5?
5.A solenoid of radius R and length l m has N turns of wire. What is the self-inductance of the solenoid? If the current is l, what is the energy stored in the solenoid?
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