In the picture the two wires carry current i1 and i2, respectively, with positiv

Question

In the picture the two wires carry current i1 and i2, respectively, with positive current to the right. The charge q is positive and has velocity v to the right. Select True or False for the following statements. If i1 = 0 and i2 is greater than zero, then the magnetic field near charge q points into the page. If i2 = 0 and i1 = 0 is greater than zero, then the force on q is to the top of the page. If i1 = 0 and i2 is greater than zero, then the force on q points out of the page. If i1 is greater than i2, then the force on q is to the top of the page. If v = 0, then the force on q is zero.

Explanation / Answer

The first statement is false. If i1 = 0, it has no magnetic field so we can eliminate it from consideration.

For i2, then, apply the right hand rule for a current carrying wire. Place your thumb in the direction of the current and then your fingers wrap in the direction of the magnetic field around the wire. It is then shown that the magnetic field near point q will point out of the page.

For statement 2, again using the right hand rule for a current carrying wire, you can see that the magnetic field near point q points into the page.

Then you have to apply the next right hand rule (for a charge moving in a magnetic field). Place your fingers in the direction of the field (into the page) and your thumb in the direction of the velocity of the charge (to the right), the force will come out of your palm (which will be upward)

So statement 2 is true, the force is upward toward the top of the page.

For statement 3 again using the right hand rule for a current carrying wire, you can see that the magnetic field near point q points out of the page.

Then you have to apply that second right hand rule (for a charge moving in a magnetic field). Place your fingers in the direction of the field (out of the page) and your thumb in the direction of the velocity of the charge (to the right), the force will come out of your palm (which will be downward)

So statement 3 is false, the force is downward toward the bottom of the page, not out of the page.

For statement 4, this is the same as statement 2. i1 is greater than i2, so the same argument applies. The force will still be toward to top of the page, but the force will just not be as great as it would have been in statement 2. The statement is true.

For statement 5, the formula for finding the force is F = qvB.   If velocity is zero, then the force has to be zero, so statement 5 is true.

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