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A long straight conductor carries a current of 5 A. What is the magnetic field (in Teslas) at a distance of 7 cm from the conductor?
To calculate the magnetic field at a distance from a long straight conductor, we can use the Biot-Savart Law. However, for a long straight conductor, Ampere's Law is more convenient. The formula for the magnetic field (B) around a straight conductor is given by:
B = (μ₀ * I) / (2 * π * r)
where:
- B is the magnetic field in Teslas (T)
- μ₀ is the permeability of free space, which is approximately 4π × 10^(-7) Tm/A
- I is the current in Amperes (A)
- r is the distance from the conductor in meters (m)
Given the current (I) is 5 A and the distance (r) is 7 cm (0.07 m), we can calculate the magnetic field (B):
B = (4π × 10^(-7) Tm/A * 5 A) / (2 * π * 0.07 m)
B = (20π × 10^(-7) Tm) / (0.14 m)
B ≈ 0.000142857 T
So, the magnetic field at a distance of 7 cm from the conductor is approximately 1.43 × 10^(-4) Teslas.
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] | 8 |
"A concave lens with a focal length of 10 cm is placed 15 cm away from an object. Find the image distance and magnification of the object."
To find the image distance and magnification of the object, we can use the lens formula and magnification formula.
The lens formula is given by:
1/f = 1/u + 1/v
where f is the focal length, u is the object distance, and v is the image distance.
For a concave lens, the focal length is negative. So, f = -10 cm.
The object distance, u = -15 cm (negative because the object is on the same side as the light source).
Now, we can plug these values into the lens formula:
1/(-10) = 1/(-15) + 1/v
To solve for v, we can first find the common denominator:
(-15 - 10) / (10 * 15) = 1/v
-25 / 150 = 1/v
Now, we can take the reciprocal of both sides to find v:
v = -150 / 25
v = -6 cm
The image distance is -6 cm, which means the image is formed 6 cm in front of the lens on the same side as the object.
Now, let's find the magnification using the magnification formula:
M = -v/u
M = -(-6)/(-15)
M = 6/15
M = 2/5
The magnification of the object is 2/5 or 0.4. This means the image is 0.4 times the size of the object and is diminished and upright since the magnification is positive.
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"A current-carrying rectangular sheet of dimensions 4m x 2m carries a current of 5A in the positive (...TRUNCATED) | 88 | [-0.005174081772565842,-0.0025942723732441664,-0.021949296817183495,-0.016176480799913406,0.01049392(...TRUNCATED) | 8 |
"What is the magnitude and direction of the magnetic field at a distance of 2 cm from a current-carr(...TRUNCATED) | 127 | [-0.018959399312734604,-0.014011887833476067,-0.023624006658792496,-0.018551025539636612,0.013943738(...TRUNCATED) | 8 |
"A current-carrying inductor has an inductance of 2 H and carries a current of 3 A. What is the magn(...TRUNCATED) | 164 | [-0.0008083388092927635,-0.005700996611267328,-0.017548473551869392,-0.03097669966518879,-0.00155834(...TRUNCATED) | 8 |
"A square loop of side length 0.2 m is carrying a current of 3 A. What is the magnetic field at the (...TRUNCATED) | 213 | [0.0037164699751883745,-0.021601850166916847,0.0017803136724978685,-0.01089462824165821,-0.000021104(...TRUNCATED) | 8 |
"A coaxial cable with an outer radius of 10 mm and an inner radius of 5 mm has a current of 2 A flow(...TRUNCATED) | 263 | [-0.0027201371267437935,-0.02304512821137905,-0.015581751242280006,-0.005447922274470329,-0.00727703(...TRUNCATED) | 8 |
"A transformer has a primary coil of 200 turns carrying a current of 5 A, and a secondary coil of 80(...TRUNCATED) | 266 | [-0.00652659498155117,-0.022219166159629822,-0.013575674034655094,-0.028761882334947586,-0.006025630(...TRUNCATED) | 8 |
"A rectangular loop with sides of length 10 cm and 5 cm carries a current of 2 A. What is the magnit(...TRUNCATED) | 270 | [-0.00028168389690108597,-0.032963138073682785,-0.012819839641451836,0.00242325640283525,0.017110466(...TRUNCATED) | 8 |
"A toroid has a mean radius of 10 cm, an outer radius of 15 cm and 350 turns of wire. If a current o(...TRUNCATED) | 279 | [-0.0029506476130336523,-0.00046021927846595645,-0.023915091529488564,-0.008955412544310093,0.013265(...TRUNCATED) | 8 |
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