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Physics Chapter 12 : Topic 5
Force on a Moving Charge
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The equation used to calculate the magnetic force on a moving charged particle is:
Reasoning: The magnetic force on a moving charge is given by $\mathbf{F = BqV\ sin\ \theta}$.
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In the equation $\mathbf{F = BqV\ sin\ \theta}$, the symbol $\mathbf{(q)}$ represents:
Reasoning: $\mathbf{(q)}$ represents the magnitude of electric charge moving through the magnetic field.
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The symbol $\mathbf{V}$ in $\mathbf{F = BqV\ sin\ \theta}$ represents:
Reasoning: $\mathbf{V}$ represents the speed of the moving charge.
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The magnetic force on a moving charge is maximum when:
Reasoning: At $\mathbf{\theta =}\mathbf{90}^{\mathbf{o}}$, $\mathbf{sin\ }\mathbf{90}^{\mathbf{o}}\mathbf{= 1}$, giving maximum force.
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A charged particle moving parallel to a magnetic field experiences:
Reasoning: When $\mathbf{\theta =}\mathbf{0}^{\mathbf{o}}$, $\mathbf{sin\ }\mathbf{0}^{\mathbf{o}}\mathbf{= 0}$, so no magnetic force acts.
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The SI unit of magnetic flux density $\mathbf{(B)}$ is:
Reasoning: Magnetic flux density is measured in tesla $\mathbf{(T)}$.
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If the charge of a particle is doubled while all other quantities remain constant, the magnetic force:
Reasoning: Force is directly proportional to charge. $\Longrightarrow$ $\mathbf{F}\mathbf{\propto}\mathbf{q}$
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If the velocity of a charged particle is tripled, the magnetic force will:
Reasoning: Force is directly proportional to velocity. $\Longrightarrow$ $\mathbf{F}\mathbf{\propto}\mathbf{V}$
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A charge of $\mathbf{2\ C}$ moves with velocity $\mathbf{5\ m/s}$ perpendicular to a magnetic field of $\mathbf{3\ T}$. The force is:
Reasoning: $\mathbf{F = BqV\ sin\ }\mathbf{90}^{\mathbf{o}}\mathbf{= 3 \times 2 \times 5 \times 1 = 30\ N}$
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A charged particle enters a magnetic field at an angle of $\mathbf{30}^{\mathbf{o}}$. Compared with the maximum force, the force will be:
Reasoning: $\mathbf{sin\ }\mathbf{30}^{\mathbf{o}}\mathbf{= 0.5}$ $\Longrightarrow$ So, force is half of maximum.
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The angle $\mathbf{\theta}$ in $\mathbf{F = BqV\ sin\ \theta}$ is the angle between:
Reasoning: $\mathbf{\theta}$ represents the angle between velocity of charge and magnetic field.
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A stationary charged particle placed in a magnetic field experiences:
Reasoning: If velocity $\mathbf{V = 0}$, then $\mathbf{F = Bq\ (0)\ sin\ \theta = 0}$.
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A proton and an electron enter the same magnetic field with the same velocity. The greater force acts on:
Reasoning: Magnetic force depends on magnitude of charge. Proton and electron have equal charge magnitude.
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A proton and an alpha particle move with the same velocity in the same magnetic field perpendicular to it. The larger force acts on:
Reasoning: Alpha particle has twice the charge of a proton, so it experiences greater force.
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If the magnetic field strength is doubled, the force on a moving charge:
Reasoning: Force is directly proportional to magnetic field strength.
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A charged particle moving in a magnetic field experiences no force if:
Reasoning: No force acts when velocity and magnetic field are in the same direction.
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A charged particle enters a magnetic field at $\mathbf{90}^{\mathbf{o}}$. The force acting on it is:
Reasoning: $\mathbf{sin\ }\mathbf{90}^{\mathbf{o}}\mathbf{= 1}$ $\Longrightarrow$ So, $\mathbf{F = BqV}$
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A particle with charge $\mathbf{4\ C}$ moves at $\mathbf{10\ m/s}$ in a $\mathbf{0.5\ T}$ field perpendicular to it. The force is:
Reasoning: $\mathbf{F = BqV\ sin\ }\mathbf{90}^{\mathbf{o}}\mathbf{= 0.5 \times 4 \times 10 \times 1 = 20\ N}$
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A charged particle moving through a magnetic field follows a curved path because:
Reasoning: Magnetic force acts perpendicular to velocity, changing direction but not speed.
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The magnetic force on a charged particle does not change its:
Reasoning: Magnetic force is perpendicular to velocity, so it does no work and does not change speed.
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If $\mathbf{\theta}$ changes from $\mathbf{90}^{\mathbf{o}}$ to $\mathbf{0}^{\mathbf{o}}$, the magnetic force:
Reasoning: $\mathbf{sin\ \theta}$ changes from $\mathbf{1}$ to $\mathbf{0}$, so force becomes zero.
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The direction of magnetic force on a positive charge can be found using:
Reasoning: Fleming’s left-hand rule gives the force direction on positive moving charges.
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For a negative charge moving in a magnetic field, the direction of force is:
Reasoning: Negative charges experience force opposite to the direction predicted for positive charges.
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A charged particle moves in a circular path in a magnetic field because:
Reasoning: The magnetic force provides the centripetal force needed for circular motion.
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If the velocity of a charged particle becomes zero, the magnetic force:
Reasoning: No velocity means no magnetic force.
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A charged particle moves at $\mathbf{45}^{\mathbf{o}}$ to a magnetic field. The force is:
Reasoning: $\mathbf{sin\ }\mathbf{45}^{\mathbf{o}}\mathbf{= 0.707}$ $\Longrightarrow$ So, force is $\mathbf{70.7\%}$ of maximum.
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A charge of $\mathbf{3\ C}$ moves with velocity $\mathbf{4\ m/s}$ in a magnetic field of $\mathbf{2\ T}$ at $\mathbf{90}^{\mathbf{o}}$. The force is:
Reasoning: $\mathbf{F = BqV\ sin\ }\mathbf{90}^{\mathbf{o}}\mathbf{= 2 \times 3 \times 4 \times 1 = 24\ N}$
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Which combination produces the largest magnetic force?
Reasoning: Force increases with $\mathbf{q}$, $\mathbf{V}$, $\mathbf{B}$ and is maximum at $\mathbf{90}^{\mathbf{o}}$.
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The magnetic force on a moving charge demonstrates the relationship between:
Reasoning: Moving charges create electrical current effects and interact with magnetic fields.
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A charged particle entering a uniform magnetic field with velocity perpendicular to the field will:
Reasoning: The magnetic force provides centripetal force while keeping speed constant.
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