Solving for Charge Travel Time in a Copper Rod
This section provides a step-by-step derivation to find the time ($t$) charges take to travel a distance ($d$) through a copper rod carrying a uniform current ($I$).
Relevant Physics Formulas
We utilize the following fundamental physics principles:
- The definition of electric current: $I = \frac{Q}{t}$, where $I$ is the current, $Q$ is the amount of charge, and $t$ is the time taken for the charge to flow.
- The relationship between total charge, volume charge density, and volume: $Q = \rho \times V$, where $\rho$ is the volume charge density and $V$ is the volume occupied by the charge.
- The volume of a cylindrical segment (like a portion of the rod): $V = A \times d$, where $A$ is the cross-sectional area and $d$ is the length or distance.
The temperature $T$ mentioned in the question is not relevant for calculating the time taken for charge travel based on the given parameters.
Calculation Steps
- Determine the volume ($V$) of the section of the copper rod corresponding to the distance $d$. Given the cross-sectional area $A$, the volume is: $V = A \times d$
- Calculate the total charge ($Q$) contained within this volume. Using the provided volume charge density ($\rho$): $Q = \rho \times V = \rho \times A \times d$
- Calculate the time ($t$) required for this charge $Q$ to flow, using the definition of current $I = \frac{Q}{t}$. Substitute the expression for $Q$ derived in the previous step: $I = \frac{\rho A d}{t}$ Rearrange the formula to solve for the time ($t$): $t = \frac{\rho A d}{I}$
The calculated time it takes for the charges to travel the distance $d$ is $t = \frac{\rho A d}{I}$.
Similar Questions
- A short bar magnet placed with its axis at $30^\circ$ with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \text{ J}$. The value of $\alpha$ is ______.
- An electromagnetic wave of frequency $100\text{ MHz}$ propagates through a medium of conductivity, $\sigma = 10\text{ mho/m}$. The ratio of maximum conduction current density to maximum displacement current density is __________.
$\left[ \text{Take } \frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\text{ Nm}^2\text{/C}^2 \right]$ - An inductor stores $16\text{ J}$ of magnetic field energy and dissipates $32\text{ W}$ of thermal energy due to its resistance when an a.c. current of $2\text{ A}$ (rms) and frequency $50\text{ Hz}$ flows through it. The ratio of inductive reactance to its resistance is _________. ($\pi = 3.14$)
- A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^\circ$ with vertical, then maximum induced EMF between the point of suspension and point of oscillation is ___________ mV. (Take $g = 10\text{ m/s}^2$)
Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for $V = 5\sin(100t)$ The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ___________ $\mu\text{F}$.
The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants $K_1 = 2$, $K_2 = 3$ and $K_3 = 5$ (as shown in figure). If new capacitance is $\frac{n}{3}C$ then the value of $n$ is ___________.
- The equation of the electric field of an electromagnetic wave propagating through free space is given by : $E = \sqrt{377} \sin(6.27 \times 10^3 t - 2.09 \times 10^{-5} x)\text{ N/C}$
The average power of the electromagnetic wave is $\left(\frac{1}{\alpha}\right)\text{ W/m}^2$. The value of $\alpha$ is ___________.
$\left[ \text{Take } \sqrt{\frac{\mu_0}{\epsilon_0}} = 377\text{ in SI units} \right]$ Combination of four parallel plate air capacitors is shown in figure. Separation between the plate P1 & P2 is $\frac{d}{3}$ and separation between the plates P2 and P3 is d.
The equivalent capacitance of the configuration is _____________$\mu$F.
(Given $\frac{\epsilon_0 A}{d} = 4\mu$F . Where A=Area of plates)
- A plane polarized monochromatic EM wave is traveling in vacuum along z direction such that at $t = t_1$ it is found that the electric field is zero at a spatial point $z_1$. The next zero that occurs in its neighbourhood is at $z_2$. The frequency of the electromagnetic wave is :
A copper rod of mass m slides under gravity on two smooth parallel rails, with separation $l$ and set at an angle of $\theta$ with the horizontal. At the bottom, rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is :
Important Questions from Electricity and Magnetism
- A short bar magnet placed with its axis at $30^\circ$ with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \text{ J}$. The value of $\alpha$ is ______.
- An electromagnetic wave of frequency $100\text{ MHz}$ propagates through a medium of conductivity, $\sigma = 10\text{ mho/m}$. The ratio of maximum conduction current density to maximum displacement current density is __________.
$\left[ \text{Take } \frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\text{ Nm}^2\text{/C}^2 \right]$ - An inductor stores $16\text{ J}$ of magnetic field energy and dissipates $32\text{ W}$ of thermal energy due to its resistance when an a.c. current of $2\text{ A}$ (rms) and frequency $50\text{ Hz}$ flows through it. The ratio of inductive reactance to its resistance is _________. ($\pi = 3.14$)
- A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^\circ$ with vertical, then maximum induced EMF between the point of suspension and point of oscillation is ___________ mV. (Take $g = 10\text{ m/s}^2$)
Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for $V = 5\sin(100t)$ The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ___________ $\mu\text{F}$.
