10 pts: Magnetic Field Questions

Question

1) Find the magnitude of the force on a straight 1m wire with a current of 2A at an angle of 45 degrees to a .7T uniform magnetic field.

2) Find the magnitiude of the magnetic field .4m from a straight wire with 5A current.

3) Two objects with equal charge have a mass of 3 x 10^4 kg. Find the possible charges on each object if the electric force cancels the gravitational force between each object.

Any help would be appreciated, since my textbook doesn't provide the solutions to these questions, so I have nothing to check my answers against.

Answer 1

1) The force on a wire is given by F = ILB sin θ

F = 2 A x 1 m x 0.7 T x sin(45°) = 1 N

2) The magnetic field at a distance r away from a long, straight wire is given by B = µ₀I / 2πr

B = ((4π x 10^-7 Tm/A) x 5 A) / (2π x 0.4 m) = 2.5 µT

3) Gravitational force is given by F = Gm1m2 / r² and electrostatic force is given by F = kq1q2 / r². If they are equal, then solve for the charge.

(Gm1m2 / r²) = (kq1q2 / r²)

Gm² = kq²

q² = Gm² / k

q = (Gm² / k)^(1/2)

= (((7 x 10^-11 Nm²/kg²) x (3 x 10^4 kg)²) / (9 x 10^9 Nm²/C²))^(1/2)

= 3 µC