The current I through a long solenoid with n turns per meter and radius R is changing with time as given by dI/dt. Calculate the induced electric field as a function of distance r from the central axis of the solenoid.

The current I through a long solenoid with n turns per meter and radius R is changing with time as given by dI/dt. Calculate the induced electric field as a function of distance r from the central axis of the solenoid.

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter31: Inductance

Section: Chapter Questions

Problem 4P

See similar textbooks

Related questions

Q: The long wire AB carries a current that is increasing at a constant rate dildt . B dr (a) At the…

Q: A solenoid of a radius R wound with n turns per unit lengthcarries a current given by I = I0e −βt,…

A: The magnetic field due to solenoid is,

Q: The current in a long solenoid varies as I(t) = Io sin(ωt). Use Faraday’s law to find the induced…

Q: (a) At what angle θ is the torque on a current loop 90.0% of maximum? (b) 50.0% of maximum? (c)…

A: The expression for maximum torque is given by, τmax=NIABsinθ (a) Thus when the torque on a current…

Q: A long solenoid has N turns, a length L and a circular cross section with a radius R. If the current…

Q: The current I = Io sin(wt) through a long solenoid with n turns per meter and radius R is changing…

Q: A long solenoid has a radius of 4 cm and has 800 turns/m. If the current in the solenoid is…

Q: A long solenoid with a circular cross section has n turns per unit length and radius R. The current…

A: step-1*A long solenoid with circular cross-section hes 'n' turns per unit length.*The current…

Q: A loop of radius a = 9.5 cm lays in the x-y plane, in a region of uniform, time-dependent magnetic…

A: Radius of circular loop (R) = 9.5 cm = 0.095 m Magnetic field ( B[t]) = 1.6 t Resistance (R) = 4.1…

Q: A long solenold with a circular cross section has n turns per unit length and radlus R The current…

A: We know that, magnetic field (B) outside a long solenoid can never be zero. Because a solenoid of…

Q: For the next two items, consider a thin conducting rod of length L riding along two parallel…

A: Given problem is related to megnetic feild effect.

Q: An aluminum ring of radius r1 = 5.00 cm and resistance 3.00 x 10-4 V is placed around one end of a…

A: Given Data: The radius of the aluminum ring is, r1=5.00 cm The radius of a solenoid is, r2=3.00 cm…

Q: A rectangular coil with dimensions a and b and resistance R = 6N is placed in a uniform magnetic…

Q: The figure shows a wire segment of length As = 3.5 cm, centered at the origin, carrying current i=…

A: According to Bartleby guidelines, I can answer maximum three subparts. If you want help with other…

Q: A conducting rectangular loop (stationary) of single turn lies on the xy plane as shown in the…

Q: Determine the current I flowing through a solenoid, if the magnetic flux inside its core is found to…

A: The magnetic flux in the coil can be determined as, Here, B and A represent the magnetic field and…

Q: An h by w rectangular conducting loop is situated in a charging magnetic field B = B,sinwtây. The…

A: Given quantities: Magnetic field (B) = B0sin(ωt)ax length of the loop = h width of the loop = w Let,…

Q: Determine the current I flowing through a solenoid, if the magnetic flux inside its core is found to…

Q: In Figure (a), a circular loop of wire is concentric with a solenoid and lies in a plane…

Q: A rectangular surface of length 3.25 cm and width 5.25 cm lies on the x-y planes at z=0. What is the…

A: Length of rectangular surface l = 3.25 cm = 3.25×10-2 m Width of rectangular surface w = 5.25 cm =…

Q: For a toroidal solenoid with the average circumference L =10 cm and 200 coils, the current is 100…

Q: A rectangular loop of wire with total resistance R = 1500 N is fixed in place near an infinitely…

A: Given:- A rectangular loop of wire with total resistance R 1500 12 is fixed in place near an…

Q: A rectangular coil with dimensions a and b and resistance R = 60 is placed in a uniform magnetic…

Q: In Fig. a, two circular loops, with different currents but the same radius of r, are centered on the…

A: To determine: Expression for current i1 in loop 1. Expression for current i2 in loop 2.

Q: The magnetic moment pm = 1 (A / m2 ) has the angle O = 30 to the magnetic field. The torque acting…

Q: An aluminum ring of radius 5.00 cm and resistance 3.00 × 10–4 O is placed on top of a long air-core…

A: Aluminium ring radius, r2 = 5 cm = 0.05 m Aluminium ring resistance, R = 3×10-4 ῼ solenoid coil…

Q: A long solenoid with a circular cross section has n turns per unit length and radius R. The current…

Q: By how much is the approximation B = μ0 nI in error at the center of a solenoid that is 15.0 cm…

A: Given data The length of the solenoid is L=15 cm The diameter is, d=4.0 cm The approximate magnetic…

Q: A long solenoid has a radius of 4 cm and has 800 turns/m. If the current in the solenoid is…

A: option (e) is correct.

Q: A rectangular coil with dimensions a and b and resistance R = 6N is placed in a uniform magnetic…

Q: A conductor, 10 cm in length, moves with a uniform velocity of 2 m/s at right angles to itself and…

A: This question is based on Motional emf concept. When a conductor moves in an external Magnetic…

Q: In a given region of space, the vector magnetic potential is giv A = x5 cos zy + z(0.2+sin zx)…

A: Given- A→=x^5cosπy+z^(0.2+sinπx) mWb/m

Q: Find the magnitude and direction of the induced emf around the rectangular loop of sides a and b as…

Q: A long solenoid with 8.00 x 102² turns per meter and radius 2.00 cm carries an ocillating current I…

Concept explainers

Ferromagnetism

Ferromagnetism is a mechanism by which some materials show magnetic properties. Iron and magnetite, an oxide of iron, are two naturally occurring materials that show the property of ferromagnetism. The word ferromagnetism is derived from the Latin name of iron, "Ferrum" as it was the first observed material to show such property. The property of ferromagnetism is shown by only a few substances such as iron, nickel, cobalt, and their alloys. Some transition metals and alloys of rare-earth metals also show ferromagnetism.

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Show that the expression for the magnetic field of a toroid reduces to tlrat for the field of an infinite solenoid in the limit that the cenmal radius goes to infinity.
A square loop with side length L, mass M, and resistance R lies in the xy plane. A magnetic field B = B0(y/L) k is present in the region of the space near the loop. Determine the magnitude and direction of the induced current in the loop as the loop starts moving at velocity v = B0(y/L) j.
The magnetic flux through a metal ring varies with time t according to (B = at3 bt2, where (B is in webers, a = 6.00 s3, b = 18.0 s2, and t is in seconds. The resistance of the ring is 3.00 . For the interval from t = 0 to t = 2.00 s, determine the maximum current induced in the ring.
By how much is the approximation B=0nI in error at the center of a solenoid that is 15.0 cm long, has a diameter of 4.0 cm, is wrapped with n turns per meter, and carries a current I?
A conducting single-turn circular loop with a total resistance of 5.00 is placed in a time-varying magnetic field that produces a magnetic flux through the loop given by B = a + bt2 ct3, where a = 4.00 Wb, b = 11.0 Wb/s2, and c = 6.00 Wb/s3. B is in webers, and t is in seconds. What is the maximum current induced in the loop during the time interval t = 0 to t = 3.50 s?
A flat loop of wire consisting of a single turn of cross-sectional area 8.00 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 T to 2.50 T in 1.00 s. What is the resulting induced current if the loop has a resistance of 2.00 ?
A thin conducting bar (60.0 cm long) aligned in the positive y direction is moving with velocity v=(1.25m/s)i in a region with a spatially uniform 0.400-T magnetic field directed at an angle of 36.0 above the xy plane. a. What is the magnitude of the emf induced along the length of the moving bar? b. Which end of the bar is positively charged?
A long solenoid has N turns, a length L and a circular cross section with a radius R. If the current varies as I(t), then what is the induced electric field as a function of radius r? In terms of r<R and r >R? Write the expression for dB/dt in terms of I(t).
A long solenoid of radius a with n turns per unit length is carrying a time-dependent current I(t) = I0 sin ωt where I0 and ω are constants. The solenoid is surrounded by a wire of resistance R that has two circular loops of radius b with b > a . Find the magnitude and direction of current induced in the outerloops at time t = 0 .
The magnetic field strength at an arbitrary point PP on the axis of a circular loop of radius a� carrying current I� is given by Using this equation, find the magnetic field strength at the center of the solenoid’s axis for a solenoid of finite length l and cross-sectional radius a .
When the Hemholtz distance condition is satisfied the second derivative of the magnetic field with respect to z vanishes or becomes zero at the center ( point P). Show that both d2Bz/dz2 = 0 and d3Bz/dz3 = 0 at point P.
A rectangular wire loop with length a and width b lies in the xy-plane, as shown below. Within the loop there is a time-dependent magnetic field given by B → (t) = C (x cos ωt)i ^ + (y sin ωt)k ^, with B → (t) in tesla. Determine the emf induced in the loop as a function of time.