A long straight wire carries current I = 5.0 A in the direction shown in the ske
ID: 3891962 • Letter: A
Question
A long straight wire carries current I = 5.0 A in the direction shown in the sketch. A small sphere with negative charge q = -8.0 times 10-6 C is 0.20 m from the wire and is moving parallel to the wire in the direction opposite to the current direction. The speed of the sphere is v = 40.0 m/s. What are the magnitude and direction of the magnetic field of the wire at the location of the sphere? (The direction is one of the following: into the page, out of the page, toward the top of the page, toward the bottom of the page, to the left or to the right.) What are the magnitude and direction of the force that the wire exerts on the sphere? (The direction is one of the following: into the page, out of the page, toward the top of the page, toward the bottom of the page, to the left or to the right.)Explanation / Answer
Magnetic field due to wire at sphere = mu_o*I/2*pi*r = 1.25*10^-6 * 5 / 2*3.14*0.2 = 5*10*-6 T
Direction out of the plane of paper.
Use right hand, place your thumb on wire in current carrying direction, curl your fist. Direction in which fist curls gives the direction of B.
Force experienced by sphere = q*(|v||B|sin(theta)) =8*10^-6 *(40)*5*10*-6 = 1.6*10^-9 N
Direction - towards downside of the page
Use cross product rule
Keep your thumb, first finger and middle finger perpendicular to each other.
Align your first finger in direction of velocity, middle to the direction to B, then thumb gives the direction of force. Since the charge here is negative so the direction of force will be reverse of what you get from this.
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