Question

In: Physics

A four-turn circular wire coil of radius 0.550 m lies in a plane perpendicular to a...

A four-turn circular wire coil of radius 0.550 m lies in a plane perpendicular to a uniform magnetic field of magnitude 0.355 T. If the wire is reshaped from a four-turn circle to a two-turn circle in 0.128 s (while remaining in the same plane), what is the average induced emf in the wire during this time?

Solutions

Expert Solution

According to the given problem,

We know that,

Induced EMF   E   =   -dφ/dt   =   - B *dA/dt   =   - B * (A2 -A1) / dt   =   B *(A1   -   A2) /dt

Given,

B   =   Magneticfield   =   0.355 T,   

   In reshaping of wire, circumference ( totallength) must remain the same.

   When wire is in four loops,   totallength   L   = 4 *(2 * π *r1 )  = 8 *π *0.55 = 13.823 m

   When wire is in two loop   L   = 2(2 *π *r2) =>   r2   = 13.823/4*π = 1.1 m

   Initialarea   A1   =   No.of loops * π *r12   = 4 *3.14 *0.552   = 3.80133 m2

   Finalarea   A2   = No.of loops* π*r22   = 2* 3.14*1.12   = 7.6027 m2

   Hence inducedEMF   E   =   0.355 *( 3.80133  -   7.6027) /0.128 =    - 10.543 V

   - ve sign idicates the direction of inducedEMF.


Related Solutions

A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of...
A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of the field is changing, so that an emf of 0.25 V and a current of 2.5 A are induced in the coil. The wire is then re-formed into a single-turn square coil, which is used in the same magnetic field (again perpendicular to the plane of the coil and with a magnitude changing at the same rate). What (a) emf and (b) current are...
A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of...
A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of the field is changing, so that an emf of 0.81 V and a current of 3.8 A are induced in the coil. The wire is then re-formed into a single-turn square coil, which is used in the same magnetic field (again perpendicular to the plane of the coil and with a magnitude changing at the same rate). What (a) emf and (b) current are...
A 20-turn circular coil of radius 4.20 cm and resistance 1.00 Ω is placed in a magnetic field directed perpendicular to the plane of the coil.
A 20-turn circular coil of radius 4.20 cm and resistance 1.00 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.010 0t + 0.040 0t2, where B is in teslas and t is in seconds. Calculate the induced emf in the coil att = 5.40 s.
3. ​ ​Induced Emf ​A circular coil of radius 0.11 m contains a single turn and...
3. ​ ​Induced Emf ​A circular coil of radius 0.11 m contains a single turn and is located in a constant magnetic field of magnitude 0.27 T. The magnetic field has the same direction as the normal to the plane of the coil. The radius increases to 0.30 m in a time of 0.080 s. (a) Determine the magnitude of the emf induced in the coil. (b) The coil has a resistance of 0.70 ?. Find the magnitude of the...
You hold a wire coil so that the plane of the coil is perpendicular to a magnetic field vector B.
You hold a wire coil so that the plane of the coil is perpendicular to a magnetic field vector B. Vector Bis kept constant but the coil is rotated so that the magnetic field, vector B , is now in the plane of the coil. How will the magnetic flux through the coil change as the rotation occurs? Check all that apply. The flux is unchanged because the magnitude of vector B is constant. The flux increases because the angle...
A circular coil of wire with radius 4 cm and 20 turns is placed in a...
A circular coil of wire with radius 4 cm and 20 turns is placed in a uniform magnetic field of magnitude 0.3 T. The magnetic field is parallel to the area vector; i.e. perpendicular to the plane of the coil. a) What is the magnetic flux through the coil? b) The magnetic field is decreased to 0 T in 0.1 s. What is the magnitude of the emf induced in the coil during this time interval? c) If the coil...
A flat circular coil composed of 120 turns has a radius of 17.0 cm. Perpendicular to...
A flat circular coil composed of 120 turns has a radius of 17.0 cm. Perpendicular to the surface of the coil is a 3.50-T magnetic field. What is the induced emf in this coil, if the magnetic field reverses direction in 0.25 s?
A circular area with a radius of 6.60 cmcm lies in the xx-yy plane. A) What...
A circular area with a radius of 6.60 cmcm lies in the xx-yy plane. A) What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field BB = 0.211 TT that points in the +z+z direction? Express your answer in webers. B) What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field BB = 0.211 TT that points at an angle of 52.7 ∘∘ from the +z+z...
1)A circular loop of wire lies within the horizontal plane, and you are viewing it from...
1)A circular loop of wire lies within the horizontal plane, and you are viewing it from above. You hold a magnet above the loop, with its north pole up and south pole down, and you drop the magnet. In what rotational direction will you see the induced current in the loop flow? (clockwise-counterclockwise) 2)The current going through a capacitor is called a (conduction current/displacement current)and arises from changing (electric field/magnetic field) 3) semiconductors are (diamagnetic/ferromagnetic/paramagnetic) materials 4) A circular loop...
A 123 turn circular coil of radius 2.27 cm is immersed in a uniform magnetic field...
A 123 turn circular coil of radius 2.27 cm is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. Over an interval of 0.167 s , the magnetic field strength increases from 54.5 mT to 94.1 mT . Find the magnitude of the average emf avg induced in the coil during this time interval, in millivolts.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT