A straight wire in a magnetic field experiences a force of 0.028 N when the curr

Question

A straight wire in a magnetic field experiences a force of 0.028 N when the current in the wire is 2.9 A. The current in the wire is changed, and the wire experiences a force of 0.057 N as a result. What is the new current? Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field as in the figure below. Coil 1 has a radius of 4.3 cm and rotates in a 0.22-T field. Coil 2 rotates in a 0.42-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2?

Explanation / Answer

4. Force ona current carrying conductor is proportional to magnetic field and current
so, if the magnetic field is constant, and only current is changing
F1/F2 = I1/I2
0.028/0.057 = 2.9/i
i = 5.9035 A
5. Maximum torque on a current carring coil in a constant magnetic field is AIB/2 ( A is area of coil )
for same maximum torque
A1I1B1 = A2I2B2
r1^2*i1*B1 = r2^2*i2*B2
4.3^2*0.22= r2^2*0.42
r2 = 3.112 cm

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