Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismBiot-savart's & Ampere's Circuital lawMedium3 minQB

PhysicsMediumnumerical

Passage / Comprehension

Consider a conducting, uniform, thin hemispherical shell of radius $R$ , which is connected with two wires along its diameter, carrying current $I$ as shown. Neglect the field of the connecting wires. ( $I = 2$ A, $R = 1$ m.)

What is the magnetic field due to the hemisphere at its centre (in $μ$ T)?

Answer:

0.40

Solution:

Break the hemisphere into many half rings connected at the junction with external wires.
Current in each half ring:
$i = I \frac{d θ}{π}$
Field of a half ring at centre:
$\frac{μ _{0} i}{4 R}$
$B = \int_{0}^{π} \frac{μ _{0} I}{4 π R} sin θ d θ = \frac{μ _{0} I}{2 π R} = 0.40 μ$ T
Printed key: 0.40.

Subject:PhysicsTopic:MagnetismSubtopic:Biot-savart's & Ampere's Circuital law

⏱ 3mℹ️ Source: QB

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