In the picture below, the two wires carry current i 1 and i 2 , respectively, wi

Question

In the picture below, the two wires carry current i1 and i2, respectively, with positive current to the right. The charge q is positive, is located midway between the wires, and has velocity v to the right.

Which of the following are true?

A) If i1 = 0 and i2 is greater than zero, then the force on q points out of the page.

B) If i1 = - i2, then the force on q is zero.

C) If i1 is greater than i2, then the force on q is up.

D) If i1 = - i2, then the wires repel each other.

E) If i2 = 0 and i1 is greater than zero, then the magnetic field near charge q points out of the page.

F) If i2 = 0 and i1 is greater than zero, then the force on q is up.

G) If v = 0, then the force on q is zero.

Explanation / Answer

magnetic field at midway between the wires=mu*(i1-i2)/(2*pi*d)

if value is positive, direction is into the page of the paper

is value is negative, direction is out of the page of the paper

force on a moving charge=charge*cross product of velocity and magnetic field

as charge is positive, direction of force=cross product of velocity and magnetic field

if magnetic field is into the page of the paper, then force is in upward direction

if magnetic field is out of the page, force is in downward direction

A: force points either upward or downward.

hence the statement is false.

B. for force to be zero, magnetic field needs to be zero.

that will occur when i1=i2

so the statement is false.

C:

if i1>i2, field is into the page of the paper and force is upwards.

hence the statement is true.

part d:

i1=-i2, wires repel each other.

statement is true

part E:

i1>i2, field is into the page of the paper.

so statement is false.

part F:

i1>i2, force is upwards.

statement is true.

part G:

as force=charge*cross product of velocity and magnetic field

if velocity=0, force =0

statement is true.

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