A rectanglular loop consists of 6 turns of wire carrying a current of 2.2 A. The
ID: 1581765 • Letter: A
Question
A rectanglular loop consists of 6 turns of wire carrying a current of 2.2 A. The loop is in the x-y plane, and the direction of flow of the current is shown in the figure. The loop has dimensions a = 4 cm and b = 5 cm. Consider a uniform magnetic field of strength 3 × 10-4 T in x, y, or z directions.
(a) If the uniform field of 3 × 10-4 T is along the +x axis, find the magnitude of the torque acting on the loop and the total force on side a and b.
t = N-m *
HELP: The magnetic field runs parallel to the plane of the loop (or the normal to the loop is perpendicular to the magnetic field). What does this tell us about q in t = N*I*A*B*sinq?
Fa = N
2.61*10^-5 NO
Fb = N *
0 OK
(b) If the uniform field of 3 × 10-4 T is along the +y axis, find the magnitude of the torque acting on the loop and the total force on side a and b.
t = N-m *
7.92*10^-6 OK
Fa = N *
0 OK
Fb = N
6e-5 NO
(c) If the uniform field of 3 × 10-4 T is along the +z axis, find the magnitude of the torque acting on the loop and the total force on side a and b.
t = N-m *
0 OK
Fa = N
2.64*10^-5 NO
Fb = N
04 T m x y, or z A reetan ular 1 direcricna. p eon ot 16 u me of wire eam tng a current ef2.2 A e loop t8 mt e x y lane, ar the d e tom of flow of the eu ret 18 shown tn the gure he loop ha, dimonsson 4 and b 5 em on o ct a u n rm ma r tae cld of atrength (A 1fthe uniform field of 3x10 Tisalong the +x axis find the magnitude ofthe teru acting on the loop and the total force on side a and b HELP: The magnetic field ruts parallel to he plae ofthe loop (gl e nocmal to die loop is perpen acu ar to die magnebtie d), what does this tell us about in- Nyl A"B"sn ! F,-2.61 105 2.61 10 5 NO (h) I the untorm field of3x10T ia along they axis find the magninade of the torque acting an the loop and the atal farce on aide a andh N-m Reset | | Enter | -1792, 10-6 7.9210-6 OK Hoip Reet Enter ie-5 NO c) L the unit am held of 3 × 10" T 15 along tbe +z axls, ind the magmtude ofthe tolque actng on the loop taus the total force on su de·aid 0 OK F,-2.0 10-5 2.64 10-5 NO NHalp EntrExplanation / Answer
Given:
Rectangular loop contains no.of loops , N = 6
wire carrying current , I = 2.2 A
Magnetic field of strenght , B = 3 x 10-4 T
Dimensions of the loop = 4cm x 5cm
Area of the loop , A = 4cm x 5cm = 20 cm2 = 20 cm2(10-4 m2/ cm2) = 20 x10-4 m2
since, for direction of the flow of current loop is at right angle
thus, = 90o (where u given q is angle)
(a) It is known by the formula for torque acting on the loop about X- axis is ,
T = N I A B sin
= (6)(2.2 A)(20 x10-4 m2 )( 3 x 10-4 T )(sin 90o)
T = 7.92x10-6 Nm
force acting on the loop ,
Fa = I (a )( B) = Ia B sin90o
= Ia B
= (2.2 A)( 4x10-2 m)(3 x 10-4 T)
= 2.64x10-5 N
Fb = I (b xB) = Ia B sin0o
= 0 N
(b) force acting on the loop,
Fa = I (a xB) = Ia B sin0o
= 0 N
Fb = I (b x B)
= Ia B sin90o
= Ia B
= (2.2 A)( 5x10-2 m)(3 x 10-4 T)
= 3.3x10-6 N
(c) It is known by the formula for torquae acting on the loop
about Z- axis is ,
= N I A B sin
= N I A B sin0o
= 0 Nm
force acting on the loop ,
Fa or Fb = I L B sin90o
= (I)([a2 +b2])(B)
= (2.2 A)(6.40x10-2 m)(3x 10-4 T)
= 4.23x10-5 N
Hence ,
Fa = 4.23x10-5 N
Fb= 4.23x10-5 N