Magnetic Field Due To A Current Element Biot Savart Law
9 previous year questions.
Volume: 9 Ques
Yield: Medium
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Chapter Questions
9 MCQs
01
PYQ 2016
medium
physicsID: jee-main
Two identical wires and , each of length , carry the same current . Wire is bent into a circle of radius and wire is bent to form a square of side . If and are the values of magnetic field at the centres of the circle and square respectively, then the ratio is :
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4
Official Solution
Correct Option: (4)
02
PYQ 2023
hard
physicsID: jee-main
As shown in the figure, a current of flowing in an equilateral triangle of side The magnetic field at the centroid of the triangle is (Neglect the effect of earth's magnetic field)
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3
4
Official Solution
Correct Option: (4)
d = 2cm
So, the correct answer is (D) :
03
PYQ 2023
medium
physicsID: jee-main
A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cm/s. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be _____ mV.
Official Solution
Correct Option: (1)
1. Magnetic Flux: - The magnetic flux through the loop is:
where and .
2. Rate of Change of Flux: - The emf induced is:
- Differentiate with respect to time:
3. Substitute Values: -
4. Convert to mV:
Final Answer:10 mV
04
PYQ 2023
medium
physicsID: jee-main
A single current-carrying loop of wire carrying current I flows in the anticlockwise direction (seen from the +z direction) and lies in the xy plane. The plot of component of magnetic field ( ) at a distance a (less than radius of the coil) and on the yz plane vs z coordinate looks like:
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4
Official Solution
Correct Option: (1)
- At z = 0 (plane of the loop), By = 0. - By is opposite in sign for +z and -z, as per the right-hand rule.
By = 0 in plane of coil By is opposite of each other in -z and +z positions.
05
PYQ 2024
hard
physicsID: jee-main
Three vectors , , and each of magnitude are acting as shown in figure. The resultant of the three vectors is . The value of is ______.
Official Solution
Correct Option: (1)
To find the value of such that the resultant of vectors , , and is , we must first analyze the vector configuration. Given that and , use vector addition: Now sum the vectors: The resultant vector has the magnitude: Simplifying, set the magnitude equal to , telling us: Calculate: Therefore, Thus, the value of is 3, which fits within the range (3, 3).
06
PYQ 2024
medium
physicsID: jee-main
Two circular coils and of turns each have the same radius of . The currents in and are and respectively. and are placed with their planes mutually perpendicular with their centers coinciding. The resultant magnetic field induction at the center of the coils is , where ______. [Use ]
Official Solution
Correct Option: (1)
To solve the problem, we first calculate the magnetic field at the center of each coil due to the currents flowing through them. The magnetic field at the center of a single circular coil with turns, radius , and current is given by the formula: . Both coils have the same radius . For coil (with current ): . Simplifying, . For coil (with current ): . Simplifying, . The magnetic fields and are perpendicular to each other. The resultant magnetic field at the center is found using the Pythagorean theorem: . Thus, the value of is . This value falls within the expected range of 20,20.
07
PYQ 2024
hard
physicsID: jee-main
The angle between vector and the resultant of and is:
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4
Official Solution
Correct Option: (1)
The resultant vector is given by:
The angle between and is as they are in the same direction. Therefore, Option (1) is correct.
08
PYQ 2024
medium
physicsID: jee-main
Two parallel long current carrying wire separated by a distance are shown in the figure. The ratio of magnetic field at to the magnetic field produced at is . The value of is ___.
Official Solution
Correct Option: (1)
The magnetic field at point , , is given by:
The magnetic field at point , , is given by:
The ratio of magnetic fields to is:
Thus, we find:
09
PYQ 2026
medium
physicsID: jee-main
Find magnetic field at point ‘O’ in the given figure.
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4
Official Solution
Correct Option: (3)
Step 1: Understand the setup. The problem involves a circular current-carrying loop with a point located at the center of the loop. The magnetic field at the center of a circular loop of current is calculated using Ampère’s circuital law or Biot-Savart law. Step 2: Magnetic field due to a current-carrying loop. The magnetic field at the center of a circular loop of current and radius is given by the formula:
This is the magnetic field at the center due to the current circulating in the loop. Step 3: Additional considerations for the setup. In the problem, the magnetic field at point is influenced by both the current in the loop and the contribution from the straight current-carrying conductor extending to infinity. The contribution from the straight wire is calculated using Ampère’s law for a long straight current-carrying wire:
The total magnetic field at point combines the effects of both the loop and the wire. Step 4: Combine the contributions. The total magnetic field at point is:
where the first term corresponds to the magnetic field from the loop, and the second term accounts for the magnetic field contribution from the straight wire.
