Moving Charges & Magnetism Worksheets
Worksheet4.03
(Magnetic Field At The Center of Circular Current Loop)
General Instructions
Magnetic Field At The Center of Circular Current Loop
CBSE, NEET, PSEB, HSEB etc.

Ques01:
Consider a tightly wound 100 turn coil of radius 10 cm carrying a current of 1 A. What is the magnitude of the magnetic field at the center of the coil?
(NCERT)
Ques02:
The plane of a circular coil is horizontal. It has 10 turns each of radius 8 cm. A current of 2 A flows through it. The current appears to flow clockwise from a point above the coil. Find the magnitude and direction of the magnetic field at the center of the coil.
Ques03:
In the Bohr model of hydrogen atom, an electron revolves around the nucleus in a circular orbit of radius 5.1 x 10^{11} m at a frequency of 6.8 x 10^{15} Hz. What is the magnetic field set up at the center of the orbit?
Ques04:
How will the magnetic field intensity at the center of a circular current carrying coil change, if the current through the coil is doubled and the radius of the coil is halved?
Ques05:
Consider the circuit shown where APB and AQB are semicircles. What will be the magnetic field at the center O of the circular loop?
(CBSE D 1995)
Ques06:
Find the magnetic field at center O in each of the following cases. Given that both the loops in each case are coplanar and concentric.
Ques07:
The following figure shows two current carrying concentric coils each of radius R with their planes perpendicular to each other. Find the magnetic field at the center O.
Ques08:
Two identical coils P and Q each of radius R are lying in perpendicular planes such that they have a common center. Find the magnitude and direction of the magnetic field at the common center of the two coils if they carry currents equal to I and √3I respectively.
(Similar CBSE D 2012 ; CBSE F 2016 ; CBSE OD 2017)
Ques09:
A wire of length L is bent round in the form of a coil having N turns of same radius. If a steady current I flows through it in a clockwise direction, find the magnitude and direction of the magnetic field produced at its center.
(CBSE F 2009)
Ques10:
A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having n turns. If the same current passes in both the cases, find the ratio of the magnetic fields produced at the centers in the two cases.
(NEET 2016 II)
Ques11:
A wire of fixed length is turned to form a coil of one turn. It is again turned to form a coil of three turns. The same amount of current is passed in both the cases. Find the ratio of the intensities of magnetic field produced at the center of the coil.
Ques12:
A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius ‘r’ and resistance ‘R’. One of the arcs of the ring subtends an angle θ at the center. Find the value of magnetic induction at the center due to the current in the ring.
Ques13:
As shown in the figure, a cell is connected across two points A and B of a uniform circular conductor. Prove that the magnetic field at its center O will be zero.
(PSEB 1999 C)
ANSWER KEY
1. 6.28 x 10^{4} T
2. 1.57 x 10^{4} T pointing vertically downwards at the center of the coil
3. 13.4 T
4. Becomes 4 times the original field
5. Zero
6. (i) {μ_{0}I / 2} {1/R_{1} + 1/R_{2}} ⊙ (ii) {μ_{0}I / 2} {1/R_{1} – 1/R_{2}} ⊙
7. B = (µ_{0}I_{1} / 2R) î + (µ_{0}I_{2} / 2R) ĵ ;  B  = (µ_{0} / 2R) √(I_{1}^{2} + I_{2}^{2})
8. µ_{0}I/R ; The resultant magnetic field makes an angle of 30° with the horizontal
9. µ_{0}πN^{2}I/L ; The direction of magnetic field is perpendicularly inside the plane of the coil
10. 1 : n^{2}
11. 1 : 9
12. Zero for all values of θ
13. –
MCQs Quiz
Quiz on Magnetic Field At The Center of Circular Current Loop
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