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In the Bainbridge mass spectrometer (see Fig. 27.24), the magnetic-field magnitude in the velocity selector is 0.510 T, and ions having a speed of 1.82 * 106 m/s pass through undeflected. (a) What is the electric-field magnitude in the velocity selector? (b) If the separation of the plates is 5.20 mm, what is the potential difference between the plates??

Short Answer

Expert verified

a) The electric field magnitude in the velocity selector is 9.28×105V/m

b) The potential difference between the two plates is 4.83×103V

Step by step solution

01

The electric force and potential difference

The magnetic force is equal to the electric force

qvB = qE

And the potential difference across the electric field divided by the separation between the plates is equal to the electric field

E=Vd

02

Determine the electric field

(a)

The magnetic force equal to the electric force

qvB=qEE=vBThereforeE=(1.82×106m/s)(0.510T)=9.28×105V/m

Therefore, the electric field is9.28×105V/m

03

Determine the potential difference between plates

The potential difference between the two plates is

E=VdTherefore,V=Ed=(9.28×105V/m)(5.20×103m)=4.83×103V


Therefore, the potential difference between the two plates is4.83×103V

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Most popular questions from this chapter

Question: A conducting sphere is placed between two charged parallel plates such as those shown in Figure. Does the electric field inside the sphere depend on precisely where between the plates the sphere is placed? What about the electric potential inside the sphere? Do the answers to these questions depend on whether or not there is a net charge on the sphere? Explain your reasoning.

A silver wire 2.6 mm in diameter transfers a charge of 420 C in 80

min. Silver containsfree electrons per cubic meter. (a) What is the

current in the wire? (b) What is the magnitude of thedrift velocity of the

electrons in the wire?

A typical small flashlight contains two batteries, each having an emf of1.5V, connected in series with a bulb having resistance17Ω. (a) If the internal resistance of the batteries is negligible, what power is delivered to the bulb? (b) If the batteries last for1.5hwhat is the total energy delivered to the bulb? (c) The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial value? (Assume that the resistance of the bulb is constant. Actually, it will change somewhat when the current through the filament changes, because this changes the temperature of the filament and hence the resistivity of the filament wire.)

An electrical conductor designed to carry large currents has a circular cross section 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is 0.104Ω. (a) What is the resistivity of the material? (b) If the electric-field magnitude in the conductor is 1.28 V/m, what is the total current? (c) If the material has 8.5×1028free electrons per cubic meter, find the average drift speed under the conditions of part (b).

Suppose a resistor R lies alongeach edge of a cube (12 resistors in all)with connections at the corners. Find theequivalent resistance between two diagonally opposite corners of the cube (pointsa and b in Fig. P26.84).

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