Problem 4: A conducting rod spans a gap of length L = 0.179 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field B = 0.45 T pointing into the paper is in the region. The rod is moving under an external force with an acceleration a = At2, where A = 6.5 m/s4. The resistance in the wire is R = 150 2. X X X В R Randomized Variables X L = 0.179 m B = 0.45 T A = 6.5 m/s4 R = 150 2 Part (a) Express the magnitude of the magnetic flux going through the loop, , in terms of B, x and L. Expression : Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (b) Express the speed of the rod, v, in terms of A and t. Assume v 0 at t 0. Expression: V = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (c) Express the position of the rod, x, in terms of A and t. Assume x 0 at t 0. Expression : X = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (d) Express the derivative of the magnetic flux, do/dt, in terms of B, A, L and t. Expression : do/dt = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (e) Express the magnitude of the emf induced in the loop, ɛ, in terms of B, L, A and t. Expression : = 3 Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (f) Express the current induced in the loop, I, in terms of ɛ and R. Expression : I = Select from the variables below to write your expression. Note that all variables may not be required. a, B, e, 0, A, B, d, g, h, i, j, m, P, R, t x -x www
Problem 4: A conducting rod spans a gap of length L = 0.179 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field B = 0.45 T pointing into the paper is in the region. The rod is moving under an external force with an acceleration a = At2, where A = 6.5 m/s4. The resistance in the wire is R = 150 2. X X X В R Randomized Variables X L = 0.179 m B = 0.45 T A = 6.5 m/s4 R = 150 2 Part (a) Express the magnitude of the magnetic flux going through the loop, , in terms of B, x and L. Expression : Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (b) Express the speed of the rod, v, in terms of A and t. Assume v 0 at t 0. Expression: V = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (c) Express the position of the rod, x, in terms of A and t. Assume x 0 at t 0. Expression : X = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (d) Express the derivative of the magnetic flux, do/dt, in terms of B, A, L and t. Expression : do/dt = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (e) Express the magnitude of the emf induced in the loop, ɛ, in terms of B, L, A and t. Expression : = 3 Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (f) Express the current induced in the loop, I, in terms of ɛ and R. Expression : I = Select from the variables below to write your expression. Note that all variables may not be required. a, B, e, 0, A, B, d, g, h, i, j, m, P, R, t x -x www
Chapter13: Electromagnetic Induction
Section: Chapter Questions
Problem 69AP: The conducting rod shown in the accompanying figure moves along parallel metal rails that are 25-cm...
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Can you please solve d, e, f?
Transcribed Image Text:Problem 4: A conducting rod spans a gap of length L = 0.179 m and acts
as the fourth side of a rectangular conducting loop, as shown in the
figure. A constant magnetic field B = 0.45 T pointing into the paper is in
the region. The rod is moving under an external force with an
acceleration a = At?, where A = 6.5 m/s4. The resistance in the wire is R =
150 Q.
X
В
х х
R
X'
Randomized Variables
L = 0.179 m
B = 0.45 T
A = 6.5 m/s4
R = 150 Q
Part (a) Express the magnitude of the magnetic flux going through the loop, , in terms of B, x and L.
Expression :
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x
Part (b) Express the speed of the rod, v, in terms of A and t. Assume v = 0 at t = 0.
Expression :
v =
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x
Part (c) Express the position of the rod, x, in terms of A and t. Assume x = 0 at t = 0.
Expression :
X =
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x
Part (d) Express the derivative of the magnetic flux, d/dt, in terms of B, A, L and t.
Expression :
do/dt =
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x
Part (e) Express the magnitude of the emf induced in the loop, ɛ, in terms of B, L, A and t.
Expression :
= 3
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x
Part (f) Express the current induced in the loop, I, in terms of ɛ and R.
Expression :
I =
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, ɛ, 0, A, B, d, g, h, i, j, m, P, R, t
Part (g) Express the current induced in the loop, I, in terms of B, L, A, t, and R.
SchematicChoice :
BLAt³
BLAT³
BAT3
3
3R
3R
BLAt³
BLAt?
I =
2R
LAt³
I
R
R
Part (h) Calculate the numerical value of I at t = 2s in A.
Numeric : A numeric value is expected and not an expression.
I(t=2s) =
100
x ->
ww
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