Question

A) An electron and proton enter a region of uniform magnetic field, compare the magnitudes of the forces and accelerations each experience. Explain. Additionaly compare the directions of the forces if the proton and electron are moving in the same direction.

(b) • How would you orient a square current loop in a uniform magnetic field so that there is no torque on the loop?

• How would the orientation change to maximize the torque on the loop?

• In each case, is there a net magnetic force on this loop?

• Draw a diagram indicating the directions of the forces and torques on the different branches of the wire (clockwise/counterclockwise is sufficient).

(c) To minimize the effects of the magnetic field when needed, the wires carrying current to equipment or appliances are placed close together. Explain how this works to reduce the magnetic field created by the current in the wire.

Answer 1

A.

As we know that Force on a moving charge "q" with a velocity "v" in uniform magnetic field "B" is given as:

F = q * (v x B) [v x B is vector Multiplication of velocity v & Magnetic Field B]

As we know that charge on Electron and Proton are of equal magnitude but opposite in nature

So, they will experience equal but exactly opposite direction Force.

B.

As we know that Magnetic Torque on a Current carrying loop is given as:

T = i * (A x B) ; where A is area of loop and B is magnetic field. A x B is vector product of area A and Magnetic Field B

PART 1:

This force will be ZERO when A x B will be Zero, so, Perpendicular of area A is parallel of Magnetic field B.

SO, Magnetic field should Perpendicular to Plane (area) of Square Loop to have ZERO torque.

PART 2:

For maximum Torque, A x B should be maximum. It will maximum when angle between Perpendicular of area A and Magnetic field are at 90^o angle.

So, Magnetic Field will be in same plane (Area) of loop.

PART 3:

In each case, net force on loop will be ZERO as there will be equal and opposite force (i*l*B)on opposite sides of square.

PART 4: