Problem 2 Two straight fixed conducting rails form a triangle with sliding condu

Question

Problem 2 Two straight fixed conducting rails form a triangle with sliding conducting bar (shown in figure below). The conducting bar starts at the vertex at time t-0 s and moves with speed v= 5.0 m/s along them, as shown. In other words, the distance y can be expressed as y = vt. A magnetic field with B 0.5T is directed into the page ???????? x B ?????? ???????? ????????? A) Find the direction of the induced current in the sliding rail. (2 pts.) B)Find an expression for the area of the triangle enclosed by the rails and sliding bar. (5 pts.) C)Calculate the magnetic flux through the triangle at t-3.0s. (5 pts.) D) Calculate the induced emf around the triangle at t-3.0s. (5 pts.) E) If the total resistance of the triangular loop is 5.0 ? at t-3.0 s , find the current (3 pts.) BonusIf we write the induced emf as e(t)-at", where a and n are constants; Find the value of a, Find the value of n. (3 pts.)

Explanation / Answer

A) counter clockwise

B) Area of the triangle = (1/2)*base*height

= (1/2)*y*y

= y^2/2

= (v*t)^2/2

= v^2*t^2/2

C) at t = 3s,

magnetic flux through the loop = A*B

= (v^2*t^2/2)*B

= (5^2*3^2/2)*0.5

= 56.25 Weber or T.m^2

D) induced emf = the rate of magnetic flux through the loop

= B*dA/dt

= B*(v^2/2)*2*t

= B*v^2*t

at t = 3s,

induced emf = 0.5*5^2*3

= 37.5 V

E) induced current = induced emf/R

= 37.5/5

= 7.5 A

Bonus :

E(t) = B*v^2*t

a = B*v^2 = 0.5*5^2 = 12.5

n = 1

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