Answer:
Explanation:
Area of electrodes, A = 2 cm x 2 cm = 4 cm²
Separation between electrodes, d = 1 mm
Voltage, V = 9 V
(a)
Let C is the capacitance between the electrodes
C = 3.54 x 10^-12 F
Let q be the charge on each of the electrode
q = C x V
q = 3.54 x 10^-12 x 9 = 3.2 x 10^-11 C
(b)
As, the battery is disconnected the charge on the electrodes remains same.
(c)
As the battery is connected the voltage is same.
capacitance is change.
As the distance is doubled, the capacitance becomes half and the charge is also halved. q' = q/2 = 1.6 x 10^-11 C
Answer:
The magnetic force will be 0.256 N in +y direction.
Explanation:
It is given that, a wire along the z axis carries a current of 6.4 A in the z direction. Length of the wire is 8 cm. It is placed in uniform magnetic field with magnitude 0.50 T in the x direction.
The magnetic force in terms of length of wire is given by :
For direction,
So, the magnetic force will be 0.256 N in +y direction.
The diagram shows a simple electric generator. The needle that measures electric current will move back and forth between a largely positive and a large negative value.
because of that she will experience a varying electrical field, and thus a varying electric current will be zero.
The maximum positive value will occur when the wire is perpendicular to the magnetic field lines after one-fourth of rotation, and then zero.
Hence option C is correct.
The diagram shows a simple electric generator. The needle that measures electric current will move back and forth between a largely positive and a large negative value.
Learn more about electric generator here:
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1. 0.42 Hz
The frequency of a simple harmonic motion for a spring is given by:
where
k = 7 N/m is the spring constant
m = 1 kg is the mass attached to the spring
Substituting these numbers into the formula, we find
2. 2.38 s
The period of the harmonic motion is equal to the reciprocal of the frequency:
where f = 0.42 Hz is the frequency. Substituting into the formula, we find
3. 0.4 m
The amplitude in a simple harmonic motion corresponds to the maximum displacement of the mass-spring system. In this case, the mass is initially displaced by 0.4 m: this means that during its oscillation later, the displacement cannot be larger than this value (otherwise energy conservation would be violated). Therefore, this represents the maximum displacement of the mass-spring system, so it corresponds to the amplitude.
4. 0.19 m
We can solve this part of the problem by using the law of conservation of energy. In fact:
- When the mass is released from equilibrium position, the compression/stretching of the spring is zero: , so the elastic potential energy is zero, and all the mechanical energy of the system is just equal to the kinetic energy of the mass:
where m = 1 kg and v = 0.5 m/s is the initial velocity of the mass
- When the spring reaches the maximum compression/stretching (x=A=amplitude), the velocity of the system is zero, so the kinetic energy is zero, and all the mechanical energy is just elastic potential energy:
Since the total energy must be conserved, we have:
5. Amplitude of the motion: 0.44 m
We can use again the law of conservation of energy.
- is the initial mechanical energy of the system, with
being the initial displacement of the mass and
being the initial velocity
is the mechanical energy of the system when x=A (maximum displacement)
Equalizing the two expressions, we can solve to find A, the amplitude:
6. Maximum velocity: 1.17 m/s
We can use again the law of conservation of energy.
- is the initial mechanical energy of the system, with
being the initial displacement of the mass and
being the initial velocity
is the mechanical energy of the system when x=0, which is when the system has maximum velocity,
Equalizing the two expressions, we can solve to find , the maximum velocity: