   Chapter 19, Problem 30P

Chapter
Section
Textbook Problem

Mass m = 1.00 kg is suspended vertically at rest by an insulating string connected to a circuit partially immersed in a magnetic field as in Figure P19.30. The magnetic field has magnitude Bin = 2.00 T and the length ℓ = 0.500 m. (a) Find the current I. (b) If ε = 115 V, find the required resistance R. Figure P19.30

a)

To determine
The current I that passes through the circuit.

Explanation

Given info: The mass of the object suspended is 1.00kg . The magnetic field has a magnitude Bin=2.00T . The length l=0.500m .

Explanation:

The circuit is shown in the following diagram,

The magnitude of the magnetic force on a current carrying wire is given by,

Fm=BIlsinθ

• B is the magnetic field
• I is the current on the wire
• l is the length of the wire
• θ is the angle between the direction of current and the magnetic field

The gravitational force on the mass is,

Fg=mg

• m is the mass of the object hanging
• g is the free fall acceleration

The magnetic force on the left and right arm of the circuit get cancel out since they have equal magnitude and opposite direction. So the only vertical magnetic force is that on the length l . Since the angle between the magnetic field and the current is 90° ,

Fm=BIl

Since the mass is hanging in equilibrium,

Fy=

b)

To determine
The resistance R required when the voltage supply ε=115V .

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