Open Question
What is the magnetic field at the position of the dot in FIGURE EX29.6? Give your answer as a vector.
29. Sources of Magnetic Field
Magnetic Field Produced by Moving Charges
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What is the force on an electron with velocity in a region of space with magnetic field ?
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Verified step by step guidance1
Identify the given values: the velocity of the electron \( \mathbf{v} = (3.0 \times 10^5 \text{ m/s})\hat{i} + (4.0 \times 10^5 \text{ m/s})\hat{k} \) and the magnetic field \( \mathbf{B} = (2.4 \times 10^{-4} \text{ T})\hat{i} \).
Recall the formula for the magnetic force on a charged particle: \( \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \), where \( q \) is the charge of the electron, approximately \( -1.6 \times 10^{-19} \text{ C} \).
Calculate the cross product \( \mathbf{v} \times \mathbf{B} \). Since \( \mathbf{B} \) has only an \( \hat{i} \) component, the cross product will involve the \( \hat{k} \) component of \( \mathbf{v} \): \( (4.0 \times 10^5 \text{ m/s})\hat{k} \times (2.4 \times 10^{-4} \text{ T})\hat{i} = (4.0 \times 10^5 \times 2.4 \times 10^{-4}) \hat{j} \).
Simplify the cross product result to find the vector in the \( \hat{j} \) direction: \( (9.6 \times 10^1) \hat{j} \).
Substitute the cross product result into the force equation: \( \mathbf{F} = -1.6 \times 10^{-19} \text{ C} \times (9.6 \times 10^1) \hat{j} \), and simplify to find the force vector in the \( \hat{j} \) direction.
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