Question

A long, straight, current carrying wire lays within a region of space that has a magnetic field present in it, yet experiences no force. Fixing one end of the wire in place and lifting the other end up by 29° results in the wire experiencing a force. If one end of the end of the wire is then continued to be raised, what is the next angle at which the force in the wire is doubled to what was experienced at a displacement of 29°?

Answer 1

Here we have stated that,

A long, straight, current carrying wire lays within a region of space that has a magnetic field present in it, yet experiences no force which means,

The expression of force on the current carrying wire is given as,

F = ILB sin θ

Since here force is zero which means angle between B and L would be zero

Now when we fix one end of the wire in place and lifting the other end up by 29° results in the wire experiencing a force which means now the force would become

F' = ILB sin 29° = IBL × 0.4848 N

Now If one end of the end of the wire is then continued to be raised, then the next angle at which the force in the wire is doubled to what was experienced at a displacement of 29° will be given as,

F" = 2F'

Since here except angle all the quantities reaming same so that,

2 × ILB × 0.4848 = ILB Sin θ'

So form here ,

New angle θ' = (75.836)°

Which is our required angle for doubling the force as compared to 29°