A wire loop carrying a currnI1.5 A is bent into the shape of a semicircle ofradi

Question

A wire loop carrying a currnI1.5 A is bent into the shape of a semicircle ofradius R 0.5m, and a straight piece of length R, as in the figure. A uniform magnetic field B= 3.5T is applied in the plane of the loop and perpendicular to the straight edge. (35 pts) (a) Find the magnetic force (magnitude and direction) on the wire by integration. (Find general solution first and then plug in the numbers in the end). (b) (Conceptual) A negative charge moves away from a current carrying wire. What is the direction of the magnetic force on the charge? A. Left B. Right. C. To the bottom of the page. D. To the top of the page E. There is no magnetic force on the charge.

Explanation / Answer

a) magnetic force acting on a small segment of length dl on the curved part,

dF = B*I*dl*sin(theta)

total force actong on the semi circular part,
F = integral dF

= integral B*I*dl*sin(theta)

= integral B*I*R*d_theta*sin(theta) (theta = 0 to theta = 180 degrees)

= B*I*R integral sin(theta)*d_theta

= B*I*R*(-cos(theta))

= -B*I*R*( cos(theta2) - cos(theta1))

= B*I*R*(cos(theta1) - cos(theta2))

= B*I*R*(cos(0) - cos(180))

= B*I*R*(1 - (-1))

= 2*B*I*R (into the page)

magetic force acting on stright segment = B*I*R*sin(90)

= B*I*R (out of the page)

net Force, Fnet = 2*B*I*R - B*I*R

= B*I*R

= 3.5*1.5*0.5

= 2.625 N <<<<<<<-----Answer

direction : into the page

b) to the bottom of the page <<<<<<<-----Answer

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.